Question

Prove that (cos A + sin A)2 = 1 + sin 2A​

Answer 1

Answer:

Step-by-step explanation:

On LHS we have

(sinA+cosA) 2 =sin  2 A+2sinAcosA+cos  2 A  

∵sin  2 A+cos  2  A=1, we get =1+2sinAcosA    

We know, 2sinAcosA=sin2A =1+sin2A

Which is equal to RHS, hence proved.

Answer 2

Answer:

on LHS We have

(sin A + cos A) ^2

=sin ^2 + 2sin A cos A + cos ^2 A

sin ^2 A + cos ^2 A = 1 we get

= 1 +2 sin A cos A

we know 2 sin A cos A = sin 2A

= 1 + sin 2 A