Question

. If p = a cos theta+bsin theta & q = a sin theta-b cos theta
then show that a² +b^2 = p^2+q^2
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Answer 1

Answer:

p= acostheta+ bsintha

q= asintheta - bcostheta

p^ 2 = a^2cos^2theta + 2absinthetacostheta +b^2sin^2theta

q^2 =a^2sin^2theta +b^2cos^2theta -2absinthetacostheta

p^2 + q^2 = a^2cos^2theta +b^2sin^2theta +2absithetacostheta +a^2sin^2theta +b^2cos^2theta -2abcosthetasintheta

p^2 +q^2 = a^2(cos^2theta +sin^2theta) + b^2(cos^2theta +sin^2theta)

p^2 + q^2 = a^2 + b^2 [cos^2theta + sin^2theta =1 ]

hence proved