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Recent questions tagged trigonometry

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2
Maths
Can anyone please suggest any single resource which has a comprehensive list of Trigonometric Identities which might be useful to solve sums ?? (Inverses, Half angles, Double Angles, Sum rule, Product Rule etc.).
Can anyone please suggest any single resource which has a comprehensive list of Trigonometric Identities which might be useful to solve sums ?? (Inverses, Half angles, Do...
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1 votes
1 answer
4
ISI2014-DCG-54
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to $0$ $1$ $3$ $4$
The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to$0$$1$$3$$4$
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1 votes
2 answers
5
ISI2015-MMA-13
The number of real roots of the equation $2 \cos \left( \frac{x^2+x}{6} \right) = 2^x +2^{-x} \text{ is }$ $0$ $1$ $2$ infinitely many
The number of real roots of the equation$$2 \cos \left( \frac{x^2+x}{6} \right) = 2^x +2^{-x} \text{ is }$$$0$$1$$2$infinitely many
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1 votes
2 answers
6
ISI2015-MMA-27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is $0$ $1/32$ $15/32$ $10/32$
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is$0$$1/32$$...
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7
ISI2015-MMA-34
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[-1, \sqrt{3}/2]$ the interval $[- \sqrt{3}/2, 1]$ the interval $[-1, 1]$ none of the above
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1, \sqrt{3}/2]$the interval $[- \sqrt{3}/2, 1]$the interval $[-1, 1]$none of the ...
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8
ISI2015-MMA-35
If $f(x)=x^2$ and $g(x)= x \sin x + \cos x$ then $f$ and $g$ agree at no points $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two points $f$ and $g$ agree at more than two points
If $f(x)=x^2$ and $g(x)= x \sin x + \cos x$ then$f$ and $g$ agree at no points$f$ and $g$ agree at exactly one point$f$ and $g$ agree at exactly two points$f$ and $g$ agr...
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9
ISI2015-MMA-49
The polar equation $r=a \cos \theta$ represents a spiral a parabola a circle none of the above
The polar equation $r=a \cos \theta$ representsa spirala parabolaa circlenone of the above
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10
ISI2015-MMA-64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $t=0$ and $t=2 \pi$ is $2 \pi$ $2 \sqrt{2 \pi}$ $\sqrt{2 \pi}$ none of the above
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $...
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11
ISI2015-MMA-66
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid x-y \mid$ holds for all $x$ and $y$ is $2$ $1$ $\frac{\pi}{2}$ there is no smallest positive value of $K$; any $K>0$ will make the inequality hold.
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid x-y \mid$ holds for all $x$ and $y$ is$2$$1$$\frac{\pi}{2}$there ...
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2 answers
13
ISI2015-DCG-4
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is $2p$ $p^2$ $(p+1)(p-1)$ $\frac{2p}{p^2-1}$
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is$2p$$p^2$$(p+1)(p-1)$$\frac{2p}{p^2-1}$
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14
ISI2015-DCG-40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent a circle a parabola an ellipse a hyperbola
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) representa circlea ...
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1 answer
15
ISI2015-DCG-59
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in $[\:- \sqrt{3}, \sqrt{3}\:]$ $(\: – \sqrt{3}, \sqrt{3}\:]$ $(\:\frac{3}{2}, \sqrt{3}\:)$ $(\:\frac{3}{2}, \sqrt{3}\:]$
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in$[\:- \sqrt{3}, \sqrt{3}\:]$$(\: – \sqrt{3}, \sqrt{3}\:]$$(\:\frac{3}{2}, \sqrt{3}\:)$...
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1 votes
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16
ISI2015-DCG-61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is $\tan ^6 \frac{\pi}{81}$ $0$ $-1$ None of these
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is$\tan ^6 \frac{\pi}{81}$$0$$-1$None of these
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17
ISI2015-DCG-62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is$1$$2$$3$more than $3$
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1 votes
1 answer
18
ISI2015-DCG-63
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $ \sin^ {-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$ \sin^ ...
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2 answers
19
ISI2015-DCG-64
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$None of these
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2 votes
1 answer
20
ISI2015-DCG-65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is$8$$9$$9.5$None of these
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21
ISI2015-DCG-66
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals$1$$\frac{2}{5}$$\frac{3}{5}$None of these
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2 answers
22
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is $2p$ $p^{2}$ $(p+1)(p-1)$ $\frac{2p}{p^{2}-1}$
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is$2p$$p^{2}$$(p+1)(p-1)$$\frac{2p}{p^{2}-1}$
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23
ISI2016-DCG-40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ represent a circle a parabola an ellipse a hyperbola
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ representa circlea parabolaan ellipsea...
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24
ISI2016-DCG-59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in $\left[\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:-\sqrt{3},\sqrt{3}\:\right]$ $\left(\:\frac{3}{2},\sqrt{3}\:\right)$ $\left(\:\frac{3}{2},\sqrt{3}\:\right]$
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in$\left[\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:\frac{3}{...
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25
ISI2016-DCG-61
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}-1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is $\tan^{6}\frac{\pi}{81}$ $0$ $-1$ None of these
The value of $\sin^{6}\frac{\pi}{81}+\cos^{6}\frac{\pi}{81}-1+3\sin^{2}\frac{\pi}{81}\:\cos^{2}\frac{\pi}{81}$ is$\tan^{6}\frac{\pi}{81}$$0$$-1$None of these
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26
ISI2016-DCG-62
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$ $2$ $3$ more than $3$
The number of values of $x$ for which the equation $\cos x=\sqrt{\sin x}-\frac{1}{\sqrt{\sin x}}$ is satisfied is $1$$2$$3$more than $3$
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1 answer
27
ISI2016-DCG-63
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\sin^{-1}\frac{1}{\sqrt{50}}$ $\frac{\pi}{4}$
If $\sin^{-1}\frac{1}{\sqrt{5}}$ and $\cos^{-1}\frac{3}{\sqrt{10}}$ lie in $\left[0,\frac{\pi}{2}\right],$ their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$\sin^{-1}\f...
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1 answer
28
ISI2016-DCG-64
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals $1$ $1$ or $-1$ $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$ None of these
If $\cos2\theta=\sqrt{2}(\cos\theta-\sin\theta)$ then $\tan\theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$ or $1$None of these
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1 votes
2 answers
29
ISI2016-DCG-65
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is $8$ $9$ $9.5$ None of these
The value of $\sin^{2}5^{\circ}+\sin^{2}10^{\circ}+\sin^{2}15^{\circ}+\cdots+\sin^{2}90^{\circ}$ is$8$$9$$9.5$None of these
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