Trigonometry and Modelling

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Question 14

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

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

[2]

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

[2]

ci.

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

[2]

cii.

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

[2]

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

[2]

Trigonometry and Modelling Questions

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Trigonometry and Modelling

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