Amit M Agarwal Solutions for Chapter: Trigonometric Functions and Equations, Exercise 5: Target Exercises

If $\alpha +\beta +\gamma =2\pi ,$ then

If $3\sin \alpha =5\sin \beta$, then $\frac{\tan \frac{\alpha +\beta }{2}}{\tan \frac{\alpha -\beta }{2}}$ is equal to

If $\cos x-\frac{\cot \beta \sin x}{2}=\frac{\sqrt{3}}{2}$, then the value of $\tan \frac{x}{2}$ is

If the expression $n{\sin }^2\theta +2n\cos \left(\theta +\alpha \right)\sin \alpha \sin \theta +\cos 2\left(\alpha +\theta \right)$ is independent of $\theta$, then the value of $n$ is

For any real value of $\theta \ne \pi$, the value of the expression $y=\frac{{\cos }^2\theta -1}{{\cos }^2\theta +\cos \theta }$ is

Solution of equation $\left[\sin x\right]=\left[1+\sin x\right]+\left[1-\cos x\right], 0\le x\le 2\pi$ is (where $\left[.\right]$ denotes the greatest integer function)

The general solution of the equation ${\sin }^{50}x-{\cos }^{50}x=1$ is

The number of ordered pairs $\left(a,x\right)$ satisfying the equation ${\sec }^2\left(a+2\right)x+a^2-1=0,-\pi <x<\pi$is