Question

if sin theta +costheta=root2costheta show that costheta-sintheta =root 2 sin theta
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Answer 1

Answer:

Step-by-step explanation:

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............

Hence, Proved!!!!!!!

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