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3.5.6 Trigonometry (A-level only)

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Question 12

A mathematician is verifying a table of trigonometric identities for the variable α\alphaα.

a.

Using the compound angle identity for sin⁡(A+B)\sin(A + B)sin(A+B), derive the identity for sin⁡2α \sin 2\alpha\,sin2α in terms of sin⁡α \sin \alpha\,sinα and cos⁡α\cos \alphacosα.

[2]
b.

Using the compound angle identity for cos⁡(A+B)\cos(A + B)cos(A+B), derive the identity for cos⁡2α \cos 2\alpha\,cos2α in terms of sin⁡α \sin \alpha\,sinα and cos⁡α\cos \alphacosα.

[2]
ci.

Hence, write cos⁡2α \cos 2\alpha\,cos2α as an expression containing only the term cos⁡α\cos \alphacosα.

[2]
cii.

Hence, write cos⁡2α \cos 2\alpha\,cos2α as an expression containing only the term sin⁡α\sin \alphasinα.

[2]
d.

Utilize the addition formula for tan⁡(A+B)\tan(A + B)tan(A+B) to find an expression for tan⁡2α \tan 2\alpha\,tan2α in terms of tan⁡α\tan \alphatanα.

[2]

3.5.6 Trigonometry (A-level only) Questions

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