Edexcel IAL Mathematics P2.6.1 core trigonometric identities

Questions reward identity work before solving: rewrite compound angles, use sin²θ + cos²θ = 1 and convert tan, sec or cosec forms carefully.

Exam points

Rewrite compound-angle expressions using sin2θ, cos2θ or sin4θ identities.
Use sin²θ + cos²θ = 1 to find exact sin, cos or tan values from given data.
Rearrange trig equations into stated quadratic forms in sin, cos or tan.

[Maximum number: 3]

In this question you must show detailed reasoning.

Solutions relying entirely on calculator technology are not acceptable.

Show that the equation

(3 \cos \theta-\tan \theta) \cos \theta=2

can be written as

3 \sin ^{2} \theta+\sin \theta-1=0

$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow \cos \theta\left(3 \cos \theta-\frac{\sin \theta}{\cos \theta}\right)=2$

or e.g.
$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow 3 \cos ^{2} \theta-\sin \theta=2$

or e.g.
$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow 3 \cos ^{2} \theta-\frac{\sin \theta}{\cos \theta} \cos \theta=2$

M1

$3\left(1-\sin ^{2} \theta\right)-\sin \theta=2$

M1

$3 \sin ^{2} \theta+\sin \theta-1=0 *$

A1*

(3)

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P2.6.1 - Core trigonometric identities question 1