Question

If cos theta plus sin theta equals root two cos theta then show that cos theta minus sin thetaequals root2 sin theta

Answer 1

cosФ + sinФ = √2cosФ
(cosФ + sinФ)² = (√2cosФ)²
cos²Ф + sin²Ф + 2cosФsinФ = 2cos²Ф
2cosФsinФ = cos²Ф - sin²Ф = 1 - 2sin²Ф
now , (cosФ - sinФ)² = cos²Ф + sin²Ф - 2sinФcosФ = 1 - (1 - 2sin²Ф)
                                  = 2sin²Ф
∴cosФ - sinФ = √(2 sin²Ф) = √2sinФ
hence proved
pls mark as brainliest

Answer 2

Here is it answer.........

Hope it helps!