Question

If costheta+sintheta=root2 costheta. prove that costheta-sintheta=root2 sintheta

Answer 1

cos∅ + sin∅ = √2cos∅ -------(1)
take square both sides ,
cos²∅ + sin²∅ +2sin∅.cos∅ = 2cos²∅

2cos²∅ - cos²∅ - sin²∅ = 2sin∅.cos∅

cos²∅ - sin²∅ = 2sin∅.cos∅

(cos∅ - sin∅ )(cos∅ + sin∅) = 2sin∅.cos∅

put equation (1)

( cos∅ - sin∅)√2cos∅ = 2sin∅.cos∅

(cos∅ - sin∅) = √2sin∅

hence, proved //