CAIE A-Level Mathematics AS 1.5.4 Trig Identities Questions

Practise proving identities, simplifying trig expressions and rewriting equations using sin, cos, tan and Pythagorean identities.

Exam points

Prove trigonometric identities by rewriting expressions with sin, cos and tan and applying identities such as sin²θ + cos²θ = 1 and tan θ = sin θ/cos θ.
Simplify trigonometric expressions or transform equations into polynomial forms in sin θ or cos θ using appropriate identities.
Use equivalent trigonometric forms to isolate parameters or solve an equation, preserving equivalence through each algebraic step.

[Maximum number: 3]

Show that the equation $\cos \theta(7 \tan \theta-5 \cos \theta)=1$ can be written in the form $a \sin ^{2} \theta+b \sin \theta+c=0$ , where a, b and c are integers to be found.

Use identity $\tan \theta=\frac{\sin \theta}{\cos \theta}$
Use identity $\cos ^{2} \theta=1-\sin ^{2} \theta$ $\pm\left(5 \sin ^{2} \theta+7 \sin \theta-6=0\right)$

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CAIE A-Level Mathematics AS 1.5.4 Trig Identities Questions question 1