Tangent of an angle from a compound-angle difference, then the sine of its double angle
Tangent of an angle from a compound-angle difference, then the sine of its double angle
IB Year 6 | Grade 12
5 marks
The angles \(\alpha\) and \(\beta\) satisfy \(\alpha-\beta=\frac{\pi}{4}\), where \(\tan\alpha=3\).
- Find the exact value of \(\tan\beta\).[2]
- Hence find the exact value of \(\sin2\beta\).[3]
Solution:
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Answer:(a) \(\tan\beta=\frac12\) (b) \(\sin2\beta=\frac45\)
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