Vinod Singh and Shweta Pawar Solutions for Chapter: Trigonometric Functions-I, Exercise 2: Critical Thinking

If  $a {\cos }^{3 }\alpha +3a \cos \alpha {\sin }^2 \alpha =m$ and  $a\mathit{ }{\sin }^3 \alpha +3a {\cos }^{2 }\alpha \sin \alpha =n$, then  ${\left(m+n\right)}^{\frac{2}{3}}+{\left(m-n\right)}^{\frac{2}{3}}$ is equal to

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

If $p=\frac{2 \sin \theta }{1+\cos \theta +\sin \theta }$ and $q=\frac{\cos \theta }{1+\sin \theta }$, then 

If $x=\sec \varphi -\tan \varphi , y=cosec \varphi +\cot \varphi$, then 

If $\sin {\theta }_{\mathit{1}}+\sin {\theta }_2+\sin {\theta }_3=3$, then $\cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3=$ 

The equation ${\left(a+b\right)}^2=4 ab {\sin }^{2 }\theta$ is possible only when

The maximum value of $12 \sin \theta -9 {\sin }^2 \theta$ is

If $y={\sin }^2\theta +{\cos }^4\theta$, then for all real values of $\theta$