Question

prove that (cos A+ sin A)^2 =1+sin 2A​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

=>(CosA+SinA)^2=1+Sin2A

We take LHS to prove RHS

Identity :

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

$\sf= > {(CosA + SinA)}^{2} = {Cos}^{2} A+ {Sin}^{2} A+ 2SinACosA$

Formula :

$\sf \star \boxed{Sin2x=2SinxCosx}\star$

We can replace 2SinACosA by Sin2A

$\sf= > {Cos}^{2} A+ {Sin}^{2} A+ Sin2A$

$\sf\boxed{ {Sin}^{2} A + {Cos}^{2} A= 1}$

$\sf\bold{= > 1 + Sin2A}$

$\therefore$RHS=LHS (Proved)

Answer 2

Answer:

This is your answer I hope help you