Question

(sinx+cosx)^2=1+sin2x​

Answer 1

$\tt\LARGE{Hola!}$

ProoF :

$\sf \boxed{\sf{L\:H\:S}}$

$\implies\sf(\sin\theta+\cos\theta)^2$

$\implies\sf \sin^2\theta+\cos^2\theta+2\:\sin\theta\:\cos\theta$

$\implies\sf {\underline{\boxed{\sf{1+ \sin \:2\theta}}}}$

$\implies{\boxed{\sf{R\:H\:S}}}\:\:\:\:\bf{[\:Proved\:]$

__________________________

Required ConcepT :

$\mapsto\sf \sin 2\theta=2\sin\theta\:\cos\theta$

_________________

ConcepT BoosteR :

Proof of the formula sin 2x = 2 sin x cos x

$\sf We \:\:know,$

$\sf\sin(A+B)=\sin A\:\cos B\:+\cos A\:\sin B$

$\mapsto \sf\sin(x+x)=\sin x\:\cos x\:+\cos x\:\sin x$

$\mapsto \sf \sin 2x = 2\sin x\:\cos x\:\:\:\:\bf[Proved]$

__________________

HOPE THIS IS HELPFUL...