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

Verify the following:

1 + \frac{\tan^{2} β}{1 + \sec β} = \sec β

Proof:

LHS \(=\)

1 + \frac{\tan^{2} β}{1 + \sec β}

\begin{array}{l} = 1 + \frac{(\frac{i^{2} β}{i^{2} β})}{(1 + \frac{1}{i β})} \\ = 1 + \frac{i^{2} β}{\cos β (1 + \cos β)} \\ = \frac{i β + i^{2} β + \sin^{2} β}{\cos β + \cos^{2} β} \\ = \frac{\cos β + i}{\cos β (1 + \cos β)} \\ = i β \end{array}

\(=\) RHS

Thus,

1 + \frac{\tan^{2} β}{1 + \sec β} = \sec β

Hence, we proved.

Did you find an error?

6. TBQ - Prove the following III