Embibe Experts Solutions for Chapter: Trigonometric Ratios, Functions and Identities, Exercise 1: EXERCISE-1

For all $n\in N,\cos \theta .\cos 2\theta .\cos 4\theta \dots \dots \cos 2^{n-1}\theta$ equals to

If $\tan A \text{and} \tan B$ are the roots of $x^2-2x-1=0$, then ${\sin }^2\left(A+B\right)$ is

Which of the following number (s) is /are rational?

If  $\alpha$ and $\beta$ are two positive acute angles satisfying $\alpha -\beta =15°$ and $\sin \alpha =\cos 2\beta$ then the value of  $\alpha +\beta$ is equal to

If $A$ and $C$are two angles such that $A+C=\frac{3\pi }{4}$, then $(1+\cot A)(1+\cot C)$ equals -

${\log }_{t_1}\left(4\sin 9°\cos 9°\right)$ where ${\mathrm{t}}_1=4\sin 63°\cos 63°$ equals - 

If  $\left(a+b\right)\tan \left(\theta -\varphi \right)=\left(a-b\right)\tan \left(\theta +\varphi \right)$, then $\frac{\sin \left(2\theta \right)}{\sin \left(2\varphi \right)}$ is equal to -

If $\theta$ is internal angle of $n$ sided regular polygon, then $\sin \theta$ is equal to -