Question

Sin2a+cos2a=3/2 find sin4a​

Answer 1

Answer:

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Answer 2

$\sin 4a = \frac{5}{4}$

Step-by-step explanation:

Given that, $\sin 2a + \cos 2a = \frac{3}{2}$ and we have to find the value of $\sin 4a$.

Now,  $\sin 2a + \cos 2a = \frac{3}{2}$

Squaring both sides we get,

$(\sin 2a + \cos 2a)^{2} = \frac{9}{4}$

⇒ $\sin^{2}2a + \cos^{2}2a + 2\times \sin 2a \times \cos 2a = \frac{9}{4}$

⇒ $1 + \sin 4a = \frac{9}{4}$

{Since, we know the identity $\sin^{2}\theta + \cos^{2}\theta = 1$ and $2\sin \theta \cos \theta = \sin 2\theta$ }

⇒ $\sin 4a = \frac{9}{4} - 1 = \frac{5}{4}$ (Answer)