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Trigonometry and Modelling

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Question 241
a.

Given that sin⁡θ≠±1\sin \theta \neq \pm 1sinθ=±1, prove the identity

11−sin⁡θ+11+sin⁡θ≡2sec⁡2θ \frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} \equiv 2 \sec^2 \theta 1−sinθ1​+1+sinθ1​≡2sec2θ
[3]
b.

Hence, find the set of values of kkk for which the equation

11−sin⁡θ+11+sin⁡θ=k \frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} = k 1−sinθ1​+1+sinθ1​=k

has real solutions. Fully justify your answer.

[3]
c.

Given that θ\thetaθ is in the second quadrant (angle between 90∘90^\circ90∘ and 180∘180^\circ180∘) and

11−sin⁡θ+11+sin⁡θ=10\frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} = 101−sinθ1​+1+sinθ1​=10

find the exact value of tan⁡θ\tan \thetatanθ.

[3]
Markscheme

Trigonometry and Modelling Questions

  1. A Level
  2. /Maths
  3. /Trigonometry and Modelling

348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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