Question

If sinA+cosA=root over 2. then what is the value of A?

Answer 1

Answer:

sinA+cosA=root2

sin45+cos45=1/root2+1/root2

=2/root2=root2

Therefore A=45°

Answer 2

Given,

◙ sinA + cosA = √2

To find :-

The value of A.

Solution :-

$\sf{sin\ A+cos\ A=\sqrt{2}}\\\\\sf{\implies (sin\ A+cos\ A)^2=(\sqrt{2})^2}\\\\\sf{\implies sin^2 A+cos^2 A+2cos\ A.sin\ A=2}\\\\\sf{\implies 1+2cos\ A.sin\ A=2}\\\\\sf{\implies 2cos\ A.sin\ A=1}\\\\\sf{\implies sin\ 2A=1}\\\\\sf{\implies sin\ 2A=sin\ 90^\circ}\\\\\sf{\implies 2A=90^\circ}\\\\\boxed{\boxed{\sf{\implies A=45^\circ}}}$

$\rule{180}2$

Identities used :-

$\bullet\ \sf{2sinA.cosA=2sinA}$

$\bullet\ \sf{sin^2A+cos^2A=1}$