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

If \(cosec \ B+ cot \ B = q\), then prove that \(cos B= \frac{q^2 - 1}{q^2 + 1}\).

Proof:

\begin{array}{l} LHS \\ cosec B + \cot B = q \\ q = \frac{1}{i B} + \frac{\cos B}{i B} \\ squaring on both sides, we get : \\ q^{2} = \frac{1 + i B}{1 - i B} \\ q^{2} (1 - i B) = 1 + i B \\ 1 + i B = q^{2} - q^{2} i B \\ i B (1 + q^{2}) = q^{2} - 1 \end{array}

By simplifying this we get,

\(cos B =\frac{q^2 - 1}{q^2+1}\)

Did you find an error?

3. TBQ - Prove the statement