Introduction to...

If $$\displaystyle \sin \left ( A+B \right ) =\frac{\sqrt{3}}{2}$$ and $$\displaystyle \cot \left ( A-B \right )=1$$, then find $$A$$

$$\displaystyle \sec ^{4}\theta -\sec ^{2}\theta $$ in terms of $$\displaystyle \tan \theta  $$ is ___ 

The value of $$\displaystyle \left ( \sin A-\cos A \right )^{2}+\left ( \sin A+\cos A \right )^{2}$$ is _____

If $$\displaystyle \sin \left ( A+B \right )=\dfrac{\sqrt{3}}{2}$$ and $$\displaystyle \cot  \left ( A-B \right )=\sqrt{3}$$ then find the value of $$B$$.

The value of $$\displaystyle \sin 30^{\circ}\cdot \sin 45^{\circ} \cdot\text{cosec }45^{\circ}\cdot\cos 30^{\circ} $$ is ___ 

The simplified value of
$$\displaystyle \text{cosec} ^{2}\alpha \left ( 1+\frac{1}{\sec \alpha } \right )\left (1-\frac{1}{\sec \alpha }  \right )$$ is _____

If $$\displaystyle\tan \theta +\cot \theta =2 $$ find the value of $$\displaystyle \tan ^{1025}\theta +\cot ^{1025}\theta $$

If $$\displaystyle \tan \theta -\cot \theta =7  $$ find the value of $$\displaystyle \tan ^{3}\theta -\cot^{3} \theta $$

If $$\displaystyle \text{cosec}\, \theta -\cot \theta =2,$$ then find the value of $$\displaystyle \text{cosec} ^{2}\theta +\cot^{2} \theta.$$

The simplified value of $$\displaystyle \left ( \frac{1-\sin \alpha }{\cos \alpha }+\frac{\cos \alpha }{1+\sin \alpha } \right )\left ( \sec \alpha +\frac{1}{\cot \alpha } \right )$$ is _____