JEE MAIN Trigonometry Previous Year Questions (PYQs) – Page 1 of 7
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Given that the inverse trigonometric functions assume principal values only.
Let $x,y\in[-1,1]$ such that $\cos^{-1}x-\sin^{-1}y=\alpha$, with $-\dfrac{\pi}{2}\le\alpha\le\pi$.
Then, the minimum value of $x^{2}+y^{2}+2xy\sin\alpha$ is:
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Solution
If $\sin \theta + \cos \theta = {1 \over 2}$, then 16(sin(2$\theta$) + cos(4$\theta$) + sin(6$\theta$)) is equal to :
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The value of $\cos \dfrac{\pi}{22}\cdot \cos \dfrac{\pi}{23}\cdot \ldots \cdot \cos \dfrac{\pi}{210}\cdot \sin \dfrac{\pi}{210}$ is –
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Solution
Let $f_{k}(x)=\dfrac{1}{k}(\sin^{k}x+\cos^{k}x)$ where $x\in\mathbb{R}$ and $k\ge 1$.
Then $f_{4}(x)-f_{6}(x)$ equals :
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Solution
If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of
$3\sin^{2}(A+B)-10\sin(A+B)\cos(A+B)-25\cos^{2}(A+B)$ is :
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$ \text{The expression } \dfrac{\tan A}{1-\cot A,} + \dfrac{\cot A}{1-\tan A,} \text{ can be written as:} $
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Let $f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$, $x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$. Then, f is :
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Suppose $\theta\in[0,\tfrac{\pi}{4}]$ is a solution of $4\cos\theta-3\sin\theta=1$. Then $\cos\theta$ is:
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Suppose $\theta\in\left[0,\tfrac{\pi}{4}\right]$ is a solution of $4\cos\theta-3\sin\theta=1$. Then $\cos\theta$ is:
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Let $f_k(x)=\dfrac{1}{k}\left(\sin^{k}x+\cos^{k}x\right)$ for $k=1,2,3,\ldots$ Then for all $x\in\mathbb{R}$, the value of $f_4(x)-f_6(x)$ is equal to
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