Question

root over 1 + 2 sin A cos A = sin A + cos A​

Answer 1

Send root on the other side
RHS becomes
(SinA+CosA)^2

Sin^2A + Cos^2A + 2SinACosA
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(1) + 2SinACosA

This is nothing but LHS

HENCE PROVED

Answer 2

Step-by-step explanation:

$\sqrt{1 + 2 \sin\alpha \cos\alpha } = \sqrt{ { \sin }^{2} \alpha + { \cos }^{2} \alpha + 2 \sin \alpha \cos \alpha }$

as sin^2thetha + cos^2thetha=1

and we know that ;

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

here a = sin alpha

b = cos alpha

$\sqrt{ {( \sin\alpha + \cos \alpha )}^{2} }$

$= \sin( \alpha ) + \cos( \alpha )$

hence proved