Edexcel IAL Mathematics P3.2.2 further trigonometric identities

Only two direct questions exist, so focus narrowly on the identity chain: convert tan and cos terms into a quadratic in sin 2x, then solve the allowed interval.

Exam points

Convert tanθ and cosθ terms into a quadratic in sinθ using identities.
Reject impossible roots such as sin 2x = -3 before finding valid angles.

[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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P3.2.2 - Further trigonometric identities question 1