Exact value of a double-angle sine from the sum of sine and cosine

Exact value of a double-angle sine from the sum of sine and cosine

IB Year 6 | Grade 12
4 marks

It is given that \(\sin x+\cos x=\frac23\). Find, in exact form, the value of \(\sin2x\).[4]

Solution:

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Answer:\(\sin2x=-\frac59\)

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