Question

Sin4A+sin2A divide by 1+cos2A+cos4A= tan2A prove it

Answer 1

Answer:

Step-by-step explanation:

Given :

To Prove :

$\frac{sin \ 4A \ + \ sin \ 2A}{1 \ + \ cos \ 2A \ + \ cos \ 4A} = tan \ 2A$

Proof :

We know that,

sin 2A = 2 sin A cos A

cos 2A = 2 cos²A - 1

LHS = $\frac{sin \ 4A \ + \ sin \ 2A}{1 \ + \ cos \ 2A \ + \ cos \ 4A}$

⇒ $\frac{sin \ 2(2A) \ + \ sin \ 2A}{1 \ + \ cos \ 2A \ + \ cos \ 2(2A)}$

⇒ $\frac{(2 \ sin \ 2A \ cos \ 2A) \ + \ sin \ 2A}{1 \ + \ cos \ 2A \ + \ (2cos^22A \ - \ 1)}$

⇒ $\frac{(2 \ cos \ 2A \ + \ 1) sin \ 2A}{ \ cos \ 2A \ + \ 2cos^22A}$

⇒ $\frac{(2 \ cos \ 2A \ + \ 1) sin \ 2A}{(1 \ + \ 2cos \ 2A) \ cos \ 2A}$

⇒ $\frac{sin \ 2A}{cos \ 2A} = tan \ 2A$ = RHS

Hence, proved.

Answer 2

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