Question

if cos ∅ - sin ∅ =√2 sin∅, prove that cos ∅ + sin∅ =√2 cos∅

Answer 1

Here I am writing Ф as A because it is difficult for me to write Ф Always.

$Given : cos A - sin A = (\sqrt{2} sin A)$

On Squaring both sides, we get

$(cos A - sin A)^2 = ( \sqrt{2} sin A)^2$

cos^2A+ sin^2A - 2sinAcosA = 2sin^2 A

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

Add cos^2A on both sides, we get

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

2cos^2A = (cosA+sinA)^2

$\sqrt{2} cos A = (cos A + sin A)$



Hope this helps!