Amit M Agarwal Solutions for Chapter: Trigonometric Functions and Equations, Exercise 2: Work Book exercise 9.2

If $\sin \theta -\cos \theta <0,$ then $\theta$ lies between 

If $2\cos \frac{A}{2}=\sqrt{1+\sin A}+\sqrt{1-\sin A},$ then $\frac{A}{2}$ lies between $\left(n\in I\right)$

The angle $\theta$ whose cosine equals to its tangent, is given by

The value of tan $5\theta$ is

If $\left|a{\sin }^2\theta +b\sin \theta \cos \theta +c{\cos }^2\theta -\frac{1}{2}\left(a+c\right)\right|\le \frac{1}{2}k$, then $k^2$ is equal to 

If $\alpha , \beta , \gamma$ and $\delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $\lambda ,$ then the value of $4\sin \frac{\alpha }{2}+3\sin \frac{\beta }{2}+2\sin \frac{\gamma }{2}+\sin \frac{\delta }{2}$ is 

If $\tan \left(\frac{\theta }{2}\right)=\frac{5}{2}$ and $\tan \left(\frac{\varphi }{2}\right)=\frac{3}{4},$ then the value of $\cos \left(\theta +\varphi \right)$ is

If $\cos x=\tan y,\cos y=\tan z,\cos z=\tan x,$ then the value of $\sin x$ is