Prove the identities:
4sec2x−4cosec2x≡4tan2x−4cot2x4\sec^2x - 4\text{cosec}^2x \equiv 4\tan^2x - 4\cot^2x4sec2x−4cosec2x≡4tan2x−4cot2x
(5secx−5cosx)2≡25tan2x−25sin2x(5\sec x - 5\cos x)^2 \equiv 25\tan^2x - 25\sin^2x(5secx−5cosx)2≡25tan2x−25sin2x
274 exam-style questions on Edexcel A Level Maths Trigonometric Functions, covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.