If sin A + cosA =$\frac{5}{4}$, find sin2A.
If sin A + cosA =$\frac{5}{4}$, find sin2A.
अगर sin A + cosA =$\frac{5}{4}$, खोजो sin2A.
Detailed Solution & Logic
Correct Answer:
$\frac{9}{16}$
Solution:
Using the identity,
$$(\sin A+\cos A)^2=\sin^2A+\cos^2A+2\sin A\cos A$$
Since $\sin^2A+\cos^2A=1$,
$$\left(\frac{5}{4}\right)^2=1+2\sin A\cos A$$
$$\frac{25}{16}-1=2\sin A\cos A$$
$$\frac{9}{16}=2\sin A\cos A$$
Now,
$$\sin 2A=2\sin A\cos A=\frac{9}{16}$$
Hence, the required value is
$\frac{9}{16}$
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