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

If $\theta =\frac{\pi }{8},$ then what is the value of $(2\cos \theta +1{)}^{10}(2\cos 2\theta -1{)}^{10}(2\cos \theta -1{)}^{10}$$(2\cos 4\theta -1{)}^{10}?$

Let $\theta$ be a positive angle. If the number of degrees in $\theta$ is divided by the number of radians in $\theta ,$ then an irrational number $\frac{180}{\mathrm{\pi }}$ results. If the number of degrees in $\theta$ is multiplied by the number of radians in $\theta ,$ then an irrational number $\frac{125\pi }{9}$ results. The angle $\theta$ must be equal to 

The value of $\tan 9°-\tan 27°-\tan 63°+\tan 81°$ is equal to

The value of $\sqrt{3}cosec20°-\sec 20°$ is equal to

Angle $\alpha$ is divided into two parts $A$ and $B$ such that $A-B=x$ and $\tan A:\tan B=p:q$. The value of $\sin x$ is equal to

If $\sec (\theta -\alpha ), \sec \theta$ and $\sec (\theta +\alpha )$ are in $\mathrm{AP},$ where $\cos \alpha \ne 1,$ then what is the value of ${\sin }^2\theta +\cos \alpha ?$

In triangle $ABC$, if $\frac{{\sin }^{2}A+{\sin }^{2}B+{\sin }^{2}C}{{\cos }^{2}A+{\cos }^{2}B+{\cos }^{2}C}=2$, then the triangle is

If $\cos A\cos B\cos C=-\frac{1}{2}$ and $A=C$ in a triangle $ABC$ then $\cos 2A$ is equal to