G Tewani Solutions for Chapter: Trigonometric Functions, Exercise 1: DPP

If $\frac{{\sin }^{2}x-2{\cos }^{2}x+1}{{\sin }^{2}x+2{\cos }^{2}x-1}=4,$ then the value of $2{\tan }^{2}x$ is ?

If $\sin \theta , \tan \theta , \cos \theta$ are in $\mathrm{G}.\mathrm{P}.$ then $4{\sin }^2\theta -3{\sin }^4\theta +{\sin }^6\theta$

If $\tan \theta -\cot \theta =a$ and $\sin \theta +\cos \theta =b,$ then ${\left(b^2-1\right)}^2\left(a^2+4\right)$ is equal to?

The least value of $18{\sin }^2\theta +2{\mathrm{cosec}}^2\theta -3$ is:

If ${\tan }^2\alpha {\tan }^2\beta +{\tan }^2\beta {\tan }^2\gamma +{\tan }^2\gamma {\tan }^2\alpha +2{\tan }^2\alpha {\tan }^2\beta {\tan }^2\gamma =1$, then the value of ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$ is?

If $x,y,z$ are all positive acute angles, then the least value of $\tan x\left(\cot y+\cot z\right)+\tan y\left(\cot z+\cot x\right)+\tan z(\cot x+\cot y)$, is

Three circles, each of radius $1$, touch one another externally and they lie between two parallel lines. The minimum possible distance between the lines is

If $\frac{\cos \alpha }{\cos A}+\frac{\sin \alpha }{\sin A}=\frac{\cos \beta }{\cos A}+\frac{\sin \beta }{\sin A}=1$, where $\alpha$ and $\beta$ do not differ by an even multiple of $\mathrm{\pi }$, then $\frac{\cos \alpha \cos \beta }{{\cos }^{2}A}+\frac{\sin \alpha \sin \beta }{{\sin }^{2}A}=$_____