Cambridge AS & A Level. 2025. Mathematics (9709). May/June - Paper 1 (12) · Pure Mathematics 1 - Question 10

**(a)** Prove the identity $\dfrac{\tan\theta + 7}{\tan^2\theta - 3} \equiv \dfrac{\sin\theta\cos\theta + 7\cos^2\theta}{1 - 4\cos^2\theta}$.