Show the following — task. Maths CBSE Live product, Class 10 (2026-27).

Using standard trigonometric identities, Prove the following.

\((1 + \cot \beta)^2 + (1 - \cot \beta)^2 = \dfrac{2}{1 - \cos^2 \beta}\)

Proof:

\(\text{LHS}\)

\((1 + \cot \beta)^2 + (1 - \cot \beta)^2\)

= {(1 + \frac{i β}{i β})}^{2} + {(1 - \frac{i β}{i β})}^{2}

= \frac{{(i β + \cos β)}^{2}}{i^{2} β} + \frac{{(i β - \cos β)}^{2}}{i^{2} β}

= \frac{i^{2} β + \cos^{2} β + 2 \sin β i β + i^{2} β + i^{2} β - 2 i θ \cos θ}{\sin^{2} β}

= \frac{2 (\sin^{2} β + i^{2} β)}{i^{2} β}

\(=\text{RHS}\)

Did you find an error?

6. Show the following