Introduction to...

The value of $$\displaystyle \sin^{3} \alpha \left ( 1+\cot \alpha  \right )+\cos ^{3}\alpha \left ( 1+\tan \alpha  \right )$$ is equal to

The value of $$\displaystyle \sin ^{6}\theta +cos^{6}\theta+3\cos ^{2}\theta \sin ^{2}\theta $$ is

If $$\displaystyle 7\sin ^{2}\theta +3\cos ^{2}\theta =4$$ then the value of $$\displaystyle \tan \theta $$ is

If $$\displaystyle \frac{\sin x}{1+\cos x}+\frac{\sin x}{1-\cos x}=4$$ and $$\displaystyle 0^{0}\leq x\leq 90^{0}$$, then the value of $$x$$ is

If $$\displaystyle x=r\cos \alpha \cos  \beta $$ and $$y = r \cos \alpha \sin \beta$$, $$z=r$$ $$\displaystyle \sin \alpha $$ then $$\displaystyle x^{2}+y^{2}+z^{2}$$ is equal to

The value of $$\displaystyle \sin ^{2}\alpha \cos ^{2}\beta +\cos ^{2}\alpha \sin ^{2}\beta +\sin ^{2}\alpha \sin ^{2}\beta +\cos ^{2}\alpha \cos ^{2}\beta $$ is

The value of $$ \displaystyle  \sin ^{2}60^{\circ}.\cos ^{2}30^{\circ}+\tan 45^{\circ}.\cos 60^{\circ}\sin 30^{\circ}     $$ is 

If $$\displaystyle \sin \theta +co\sec \theta =2$$, then $$\displaystyle \sin^n\theta +co\sec ^{n}\theta $$ is equal to

If  $$\displaystyle \sin \theta =\dfrac12$$ and  $$\displaystyle 0^{\circ}< \theta < 90^{\circ} $$ then  $$\displaystyle \cos 2\theta =$$ _____

If co$$\displaystyle \sec \left ( 20^{\circ} + x \right )=\sec \left ( 50^{\circ}+x \right ) $$ the value of x is