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Recent questions tagged trigonometry

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TIFR Mathematics 2025 | Part B | Question: 14
There exists $\theta \in(0, \pi / 2)$ such that\[\sin \theta+\sec \theta+\cot \theta=3 .\]
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271
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NIELIT 2023 Feb Scientist C | Section D | Question: 96
The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is$2$$2 \frac{\sin 20^{\circ}}{\sin 40^{\circ}}$$4$$4 \frac{\sin 20^{\circ}}{\sin 4...
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267
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NIELIT 2023 Feb Scientist C | Section D | Question: 104
In triangle $\text{A B C}$ the value of $\angle \text{A}$ is given by $5 \cos \text{A}-3=0$, then the equation whose roots are $\sin \text{A}$ and $\tan \mathrm{A}$ is :$...
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495
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NIELIT 2023 Feb Scientist D | Section D | Question: 96
If $\sin x+\sin ^{2} x=1$ then $\cos ^{8} x+2 \cos ^{6} x+\cos ^{4} x$ equals to :$0$$-1$$1$$2$
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564
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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, Do...
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266
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Best Open Video Playlist for Trigonometry Topic | Quantitative Aptitude
Please list out the best free available video playlist for Trigonometry from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the...
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1.1k
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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$$4$
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1.8k
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ISI2015-MMA-13
The number of real roots of the equation$$2 \cos \left( \frac{x^2+x}{6} \right) = 2^x +2^{-x} \text{ is }$$$0$$1$$2$infinitely many
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ISI2015-MMA-27
Let $\cos ^6 \theta = a_6 \cos 6 \theta + a_5 \cos 5 \theta + a_4 \cos 4 \theta + a_3 \cos 3 \theta + a_2 \cos 2 \theta + a_1 \cos \theta +a_0$. Then $a_0$ is$0$$1/32$$...
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ISI2015-MMA-34
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1, \sqrt{3}/2]$the interval $[- \sqrt{3}/2, 1]$the interval $[-1, 1]$none of the ...
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757
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ISI2015-MMA-35
If $f(x)=x^2$ and $g(x)= x \sin x + \cos x$ then$f$ and $g$ agree at no points$f$ and $g$ agree at exactly one point$f$ and $g$ agree at exactly two points$f$ and $g$ agr...
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757
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ISI2015-MMA-49
The polar equation $r=a \cos \theta$ representsa spirala parabolaa circlenone of the above
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775
775 views
ISI2015-MMA-64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $...
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595
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ISI2015-MMA-66
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid x-y \mid$ holds for all $x$ and $y$ is$2$$1$$\frac{\pi}{2}$there is...
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848
848 views
ISI2015-MMA-86
The coordinates of a moving point $P$ satisfy the equations $$\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=-\sin^2x, \:\:\:\:\: t \geq 0.$$ If the curve passes through ...
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2 2 answers
1.2k
1.2k views
ISI2015-DCG-4
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is$2p$$p^2$$(p+1)(p-1)$$\frac{2p}{p^2-1}$
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1.7k
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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) representa circlea ...
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1 1 answer
1.1k
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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}\:)$$(...
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1 1 vote
1 1 answer
516
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ISI2015-DCG-61
The value of $\sin^6 \frac{\pi}{81} + \cos^6 \frac{\pi}{81}-1+3 \sin ^2 \frac{\pi}{81} \cos^2 \frac{\pi}{81}$ is$\tan ^6 \frac{\pi}{81}$$0$$-1$None of these
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428
428 views
ISI2015-DCG-62
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is$1$$2$$3$more than $3$
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1 1 answer
560
560 views
ISI2015-DCG-63
If $\sin^{-1} \frac{1}{\sqrt{5}}$ and $\cos ^{-1} \frac{3}{\sqrt{10}}$ lie in $\bigg[0, \dfrac{\pi}{2}\bigg]$, their sum is equal to$\frac{\pi}{6}$$\frac{\pi}{3}$$ \sin^ ...
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2 2 answers
615
615 views
ISI2015-DCG-64
If $\cos 2 \theta = \sqrt{2}(\cos \theta – \sin \theta)$ then $\tan \theta$ equals$1$$1$ or $-1$$\frac{1}{\sqrt{2}}, – \frac{1}{\sqrt{2}}$ or $1$None of these
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2 2 votes
1 1 answer
740
740 views
ISI2015-DCG-65
The value of $\sin ^2 5^{\circ} + \sin ^2 10^{\circ} + \sin ^2 15^{\circ} + \dots + \sin^2 90^{\circ}$ is$8$$9$$9.5$None of these
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1 1 answer
341
341 views
ISI2015-DCG-66
If $\sin(\sin^{-1} \frac{2}{5} + \cos ^{-1} x) =1$, then $x$ equals$1$$\frac{2}{5}$$\frac{3}{5}$None of these
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2 2 answers
840
840 views
ISI2016-DCG-5
If $\tan\: x=p+1$ and $\tan\; y=p-1,$ then the value of $2\:\cot\:(x-y)$ is$2p$$p^{2}$$(p+1)(p-1)$$\frac{2p}{p^{2}-1}$
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594
594 views
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$)$ representa circlea parabolaan ellipsea...
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564
564 views
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}{...
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1 1 answer
479
479 views
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
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380
380 views
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 $3$
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