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Recent questions tagged trigonometry

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31
ISI2016-DCG-66
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is $1$ $\frac{2}{5}$ $\frac{3}{5}$ None of these
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is$1$$\frac{2}{5}$$\frac{3}{5}$None of these
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1 answer
32
ISI2017-DCG-16
If $\cos x = \dfrac{1}{2}$, the value of the expression $\dfrac{\cos 6x+6 \cos 4x+15 \cos 2x +10}{\cos 5x+5 \cos 3x +10 \cos x}$ is $\frac{1}{2}$ $1$ $\frac{1}{4}$ $0$
If $\cos x = \dfrac{1}{2}$, the value of the expression $\dfrac{\cos 6x+6 \cos 4x+15 \cos 2x +10}{\cos 5x+5 \cos 3x +10 \cos x}$ is$\frac{1}{2}$$1$$\frac{1}{4}$$0$
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2 answers
33
ISI2017-DCG-17
If $\cos ^{2}x+ \cos ^{4} x=1$, then $\tan ^{2} x+ \tan ^{4} x$ is equal to $1$ $0$ $2$ none of these
If $\cos ^{2}x+ \cos ^{4} x=1$, then $\tan ^{2} x+ \tan ^{4} x$ is equal to$1$$0$$2$none of these
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1 answer
34
ISI2017-DCG-18
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to $\frac{b+c}{b-c}$ $\frac{b-c}{b+c}$ $\frac{c-b}{c+b}$ none of these
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to$\frac{b+c}{b-c}$$\frac{b-c}{b+c}$$\frac{c-b}{c+b}$none of these
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1 answer
35
ISI2017-DCG-19
The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is $\tan^{-1} (\frac{1}{2})$ $\tan^{-1} (\frac{2}{3})$ $\frac{\pi}{2}$ $\frac{\pi}{3}$
The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is$\tan^{-1} (\frac{1}{2})$$\tan^{-1} (\frac{2}{3})$$\frac{\pi}{2}$$\frac{\pi}{3...
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1 votes
1 answer
36
ISI2018-DCG-18
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as $2 \: \text{cosec} \: x$ $\text{cosec} \: x + \text{cosec} \: y$ $2 \: \sin x$ $\sin x+\sin y$
If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as$2 \: \text{cosec} \: x$$\text{cosec} \: x + \text{cosec} \: y$$2 \: \sin x$$\sin x+\...
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2 votes
1 answer
37
ISI2018-DCG-20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is $\frac{1}{18}$ $\frac{11}{6}$ $\frac{13}{6}$ $\frac{17}{6}$
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is$\frac{1}{18}$$\frac{11}{6}$$\frac{13}{6}$$\frac{17}{6}$
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1 votes
2 answers
38
ISI2016-MMA-3
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is $0$ $1$ $2$ $\infty$
The number of real roots of the equation $2 \cos \big(\frac{x^2+x}{6}\big)=2^x+2^{-x}$ is$0$$1$$2$$\infty$
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1 votes
1 answer
39
ISI MMA QROR
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n } Then lim n→∞ Gn is
For n ≥ 1, let Gn be the geometric mean of { sin (π/2 . k/n) : 1 ≤ k ≤ n }Then lim n→∞ Gn is
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2 votes
0 answers
41
ISI2011-PCB-A-1
Let $D = \{d_1, d_2, \dots, d_k\}$ be the set of distinct divisors of a positive integer $n$ ($D$ includes 1 and $n$). Then show that $\Sigma_{i=1}^k \sin^{-1} \sqrt{\log_nd_i}=\frac{\pi}{4} \times k$. hint: $\sin^{−1} x + \sin^{−1} \sqrt{1-x^2} = \frac{\pi}{2}$
Let $D = \{d_1, d_2, \dots, d_k\}$ be the set of distinct divisors of a positive integer $n$ ($D$ includes 1 and $n$). Then show that$\Sigma_{i=1}^k \sin^{-1} \sqrt{\log_...
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