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1 Pure Mathematics

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Question 9
a.

Use the identity for sin⁡(A+B)\sin(A + B)sin(A+B) to express sin⁡2A \sin 2A\,sin2A in terms of sin⁡A \sin A\,sinA and cos⁡A\cos AcosA.

[2]
b.

Use the identity for cos⁡(A+B)\cos(A + B)cos(A+B) to express cos⁡2A \cos 2A\,cos2A in terms of sin⁡A \sin A\,sinA and cos⁡A\cos AcosA.

[2]
ci.

Hence, express cos⁡2A \cos 2A\,cos2A in terms of cos⁡A\cos AcosA.

[2]
cii.

Hence, express cos⁡2A \cos 2A\,cos2A in terms of sin⁡A\sin AsinA.

[2]
d.

Use the identity for tan⁡(A+B)\tan(A + B)tan(A+B) to express tan⁡2A \tan 2A\,tan2A in terms of tan⁡A\tan AtanA.

[2]

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