Question

maths pre-board question may be comming in board plz solve

Answer 1

Given sin theta + cos theta = sqrt(2)cos theta prove cos theta - sin theta = sqrt(2)sin theta
sin theta + cos theta = sqrt(2)cos theta square both sides

sin^2theta + cos^2 theta + 2sintheta costheta=2cos^2theta
sin^2theta - cos^2theta + 2sinthetacostheta=0
-sin^2theta + cos^2theta -2sinthetacostheta=0 Add 2sin^2theta to both sides

sin^2theta+cos^2theta-2sinthetacostheta=2sin^2theta
(costheta-sintheta)^2=2sin^2theta
costheta-sintheta=sqrt(2)sintheta