Question

Prove the above mentioned question.

Answer 1

I didn't do this type of question
sorry!!

Answer 2

Solution/proof

m+n=a(cos^3theta+sin^3theta+3sintheta costheta (costheta+sin theta))

=((cos theta+sin theta)(cos^2 theta+ sin^2 theta -sin theta*cos theta)+3sin theta*cos theta (cos theta+ sin theta))

=a(cos theta + sin theta)(cos^2 theta+ sin^2 theta+2sin theta*cos theta)

==>m-n=a(cos^3 theta -sin^3 theta +3sintheta cos theta (Sin theta-cos theta))

=a(cos theta -sin theta)(cos^2 theta+ sin^2 theta +sin theta*cos theta)-3sin theta*cos theta (cos theta-sin theta))

=a(cos theta - sin theta)(cos^2 theta+ sin^2 theta-2sin theta*cos theta)

=a(cos theta- sin theta)^3

===> (m+n)^2/3+ (m-n)^2/3=a^2/3((cos theta+sin theta)^2+(cos theta -sin theta)^2)

==>a^2/3*(1+2sintheta cos theta+1-2 sintheta cos theta)

==> 2*a^2/3