If sinA + cosA = 7/5, find sin2A.

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Accepted Answer

1. Square both sides: $(\sin A+\cos A)^2=\left(	frac{7}{5}ight)^2=	frac{49}{25}$. 
2. Expand the left: $\sin^2A+\cos^2A+2\sin A\cos A=1+2\sin A\cos A$. 
3. Set equal: $1+2\sin A\cos A=	frac{49}{25}$, so $2\sin A\cos A=	frac{24}{25}$. 
4. Hence $\sin2A=2\sin A\cos A=	frac{24}{25}$.

FINAL_ANSWER: b

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