Introduction to...

If  $$\displaystyle \tan ^{2}\theta =\left ( 1-e^{2} \right )$$ then  $$\displaystyle \sec \theta +\tan ^{3}\theta\, \text{cosec}\, \theta $$ is equal to

 If $$\displaystyle a\cos ^{3}\theta +3a\cos \theta \sin ^{2}\theta =m$$ and $$\displaystyle a\sin ^{3}\theta +3a\cos ^{2}\theta \sin \theta=n$$ then $$\displaystyle \left ( m+n \right )^{\tfrac23}+\left ( m-n \right )^{\tfrac23}$$ is equal to

The value of $$\displaystyle 4\left ( \sin ^{4}30^{\circ}+\cos ^{4}30^{\circ} \right )-3\left ( \cos ^{2}45^{\circ}+\sin ^{2}90^{\circ} \right ) $$  is:

$$\displaystyle  \sin^{2} 85^{\circ} + \sin ^{2}5^{\circ} =$$ ______

If $$\displaystyle \sin ^{4}\theta +\cos ^{4}\theta =\dfrac{1}{2} $$ then the value of  $$\displaystyle \sin \theta \cos \theta  $$ is  

If $$\displaystyle  \sqrt{3}\tan \theta =3\sin \theta $$ then the value of $$\displaystyle  \sin ^{2}\theta -\cos ^{2}\theta $$ is

If $$\displaystyle a=\cos \theta +b\sin \theta =c$$, then the value of $$\displaystyle \left ( a\sin \theta -b\cos \theta  \right )$$ is

If $$\displaystyle \left ( \tan x+\sec x \right )\left ( \tan y+\sec y \right )\left ( \tan z+\sec z \right )=\left ( \sec x-\tan x \right )\left ( \sec y-\tan z \right )=K$$, then the value of $$K$$ is

If $$\displaystyle \sin \Theta +\text{cosec }\Theta =2 $$ find the value of $$\displaystyle \cot \Theta +\cos \Theta  $$

If $$\displaystyle \text{cosec}\, \theta -\cot \theta =x $$ then $$\displaystyle \text{cosec}\, \theta +\cot \theta =$$ _____