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Trigonometric Functions

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Q JEE MAIN 2021
If $e^{\left(\cos ^2 x+\cos ^4 x+\cos ^6 x+-\infty\right) \log _4 2}$ satisfies the equation $t^2-9 t+8=0$, then the value of $...
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Q JEE MAIN 2021
The number of roots of the equation, $$ (81)^{\sin ^2 x}+(81)^{\cos ^2 x}=30 $$ in the interval $[0, \pi]$ is equal to:
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Q JEE MAIN 2021
If for $x \in\left(0, \frac{\pi}{2}\right), \log _{10} \sin x+\log _{10} \cos x=-1$ and $\log _{10}(\sin x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right), n>0$, then the value of $n$...
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Q JEE MAIN_2025
The number of solutions of the equation $\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^2 \frac{5 \theta}{2}$ in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is :
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