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Recent questions tagged trigonometry

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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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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.).
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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 ... be selected as best.For the full list of selected videos please see here
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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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847
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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$15/32$10/32$
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640
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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 above
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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 $g$ agree at more than two points
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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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467
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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 $t=0$ ... $2 \pi$2 \sqrt{2 \pi}$\sqrt{2 \pi}$none of the above
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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$2$ ... $K$; any $K>0$ will make the inequality hold.
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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 ... $y=\sin 2x$y=\cos 2x+1$y=\sin ^2 x-1$
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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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783
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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 parabolaan ellipsea hyperbola
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537
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1 answers
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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}\:]$(\:\frac{3}{2}, \sqrt{3}\:)$(\:\frac{3}{2}, \sqrt{3}\:]$
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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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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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357
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1 answers
1 votes
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}}$\frac{\pi}{4}$
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334
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2 answers
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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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429
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1 answers
2 votes
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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202
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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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492
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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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342
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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 hyperbola
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370
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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]$
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272
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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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204
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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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422
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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}$
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304
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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
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374
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2 answers
1 votes
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
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