Question

＠QualityQuestion

Prove the Identity :-
4 sin(x) cos(x) = $\sf\dfrac{sin(4x)}{ cos(2x)}$​

Answer 1

ANSWER:

To Prove:

• 4 sin(x) cos(x) = sin(4x)/cos(2x)

Proof:

We need to prove that,

$\implies 4\sin x\cos x = \dfrac{\sin 4x}{\cos 2x}$

Taking LHS,

$\implies 4\sin x\cos x$

We can write 4 as, 2 * 2.

So,

$\implies 2\times2\sin x\cos x$

$\implies 2(2\sin x\cos x)$

We know that,

$\hookrightarrow 2\sin\theta\cos\theta=\sin2\theta$

So,

$\implies 2(2\sin x\cos x)$

$\implies 2\sin2x$

Multiplying and dividing by cos(2x)

$\implies 2\sin2x\times\dfrac{\cos2x}{\cos2x}$

$\implies \dfrac{2\sin2x\cos2x}{\cos2x}$

As,

$\hookrightarrow 2\sin\theta\cos\theta=\sin2\theta$

So,

$\implies \dfrac{2\sin2x\cos2x}{\cos2x}$

$\implies \dfrac{\sin(2*2x)}{\cos2x}$

$\implies\bf\dfrac{sin4x}{cos2x}=RHS$

As, LHS = RHS

HENCE PROVED!!