Embibe Experts Solutions for Chapter: Trigonometric Ratios, Functions and Identities, Exercise 1: JEE Main - 10th April 2015

If ${\sin }^2\left(10°\right)\sin \left(20°\right)\sin \left(40°\right)\sin \left(50°\right)\sin \left(70°\right)=\alpha -$ $\frac{1}{16}\sin \left(10°\right)$, then $16+{\alpha }^{-1}$ is equal to _____.

The value of $\cos \left(\frac{2\pi }{7}\right)+\cos \left(\frac{4\pi }{7}\right)+\cos \left(\frac{6\pi }{7}\right)$ is equal to

If $\cot \alpha =1$ and $\sec \beta =-\frac{5}{3}$, where $\pi <\alpha <\frac{3\pi }{2}$ and $\frac{\pi }{2}<\beta <\pi$, then the value of $\tan \left(\alpha +\beta \right)$ and the quadrant in which $\alpha +\beta$ lies, respectively are

The number of solutions of the equation $\sin x={\cos }^2 x$ in the interval $\left(0, 10\right)$ is ______.

The value of $2\sin \frac{\pi }{22}\sin \frac{3\pi }{22}\sin \frac{5\pi }{22}\sin \frac{7\pi }{22}\sin \frac{9\pi }{22}$ is equal to:

If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $\left[-\pi ,\pi \right]$ that satisfy the equation $\cos 2\theta \cos \frac{\theta }{2}=\cos 3\theta \cos \frac{9\theta }{2}$, then $mn$ is equal to _____ .

The set of all values of $\lambda$ for which the equation ${\cos }^{2}2x-2{\sin }^{4}x-2{\cos }^{2}x=\lambda$

If $\tan 15°+\frac{1}{\tan 75°}+\frac{1}{\tan 105°}+\tan 195°=2\mathrm{a}$, then the value of $\left(a+\frac{1}{a}\right)$ is :