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

Justify the following: \(\dfrac{2\sin^3 A - \sin A}{\cos A - 2\cos^3 A} = \tan A\)

Proof:

\(\text{LHS} =\)\(\dfrac{2\sin^3 A - \sin A}{\cos A - 2\cos^3 A} \)

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

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

= \frac{i A}{i A}

\( = \tan A\)

\( =\text{RHS}\)

Did you find an error?

4. prove the following