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Trigonometric Functions

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Question 141

Prove the identities:

a.

sec⁡2x−cosec2x≡tan⁡2x−cot⁡2x\sec^2x - \text{cosec}^2x \equiv \tan^2x - \cot^2xsec2x−cosec2x≡tan2x−cot2x

[2]
b.

(sec⁡x−cos⁡x)2≡tan⁡2x−sin⁡2x(\sec x - \cos x)^2 \equiv \tan^2x - \sin^2x(secx−cosx)2≡tan2x−sin2x

Hence, find the exact value of

(sec⁡π3−cos⁡π3)2 (\sec \frac{\pi}{3}-\cos \frac{\pi}{3})^2 (sec3π​−cos3π​)2
[5]
Markscheme

Trigonometric Functions Questions

  1. A Level
  2. /Maths
  3. /Trigonometric Functions

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.

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