Question

Sinthetaa+ Sin2theta/
costheta+ Cos2theta​

Answer 1

Step-by-step explanation:

Question:- Prove that sin(theta)+sin2(theta)/1+cos(theta)+cos2(theta) = tan(theta)?

Solution:-

Remamber:

$\sin(2 \theta) = 2 \sin\theta \: \cos \theta$

$\cos(2 \theta) = 2 \cos^{2} \theta - 1$

$\tan \theta = \frac{ \sin \theta}{ \cos \theta}$

Therefore,

$LHS = \frac{ \sin \theta + \sin2 \theta }{1 + \cos \theta + \cos2 \theta }$

$= \frac{ \sin \theta +2 \sin \theta \cos \theta }{1 + \cos \theta + 2\cos^{2} \theta - 1 }$

$= \frac{ \sin \theta \cancel{(1 + 2 \cos \theta )} }{ \cos \theta \cancel{(1 + 2 \cos \theta ) }}$

$= \tan \theta$

$= RHS$

:)