Question

a cos theta+b sin theta=m and a sin theta-b cos theta=n now prove that m squire+n squire=a squire+b squire​

Answer 1

Answer:

Step-by-step explana

©= Using this as theta

acos©+bsin©=m

Asin©-bcos©=n

m^2+n^2

Putting value of m and n in it

(acos©+bsin©)2+(asin©-bcos©)2

=a2cos2©+b2sin2©+2absin©cos©+a2sin©+b2cos2©-2absin©cos©

=a2cos©+b2sin2©+a2sin2©+b2cos2©

Arranging the terms

So,a2cos2©+a2sin2©+b2sin2©+b2cos2©

Takinga2 and b2 common

a2(cos2©+sin2©)+b2(sin2©+cos2©)

a2+b2 = LHS

Hence proved