If , then show that sin α + cos α = cos x.

Given

Dividing numerator And denominator on RHSBy cos α,

We know that

Consider sin α + cos α,

We know that sin(A +B) = sinA cosB + cosA sinB And cos(A +B) = cosA cosB - sinA sinB

= √2 cos x

∴ sin α + cos α = √2 cos x

Hence proved.