Edexcel A-Level Mathematics A2 P3.2.2 Further Trigonometric Identities Questions

Practise the P3.2.2 identity chain by converting cotangent and secant terms into a quadratic in cosec 2θ using trigonometric identities.

Exam points

convert cotangent and secant expressions into a quadratic in cosec 2θ using identities

[Maximum number: 4]

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Show that the equation

$2\sin\theta(3\cot^2 2\theta-7)=13\sec\theta$

can be written as

$3\operatorname{cosec}^2 2\theta-13\operatorname{cosec}2\theta-10=0$

$3\cot^2 2\theta-7=\frac{13}{2\sin\theta\cos\theta}$ $3(\operatorname{cosec}^2 2\theta-1)-7=\frac{13}{2\sin\theta\cos\theta}$ $3\operatorname{cosec}^2 2\theta-10=13\operatorname{cosec}2\theta$ $3\operatorname{cosec}^2 2\theta-13\operatorname{cosec}2\theta-10=0$

M1 dM1 ddM1 A1*

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Edexcel A-Level Mathematics A2 P3.2.2 Further Trigonometric Identities Questions question 1