" If "a cos theta+b sin theta=m" and "a sin theta-b cos theta=n," prove that "a^(2)+b^(2)=m^(2)+n^(2)

If a cos theta +bsin theta=x and a sin theta-b cos theta = y then prove that a^2+b^2=x^2+y^2

If x=a cos theta-b sin theta and y=a sin theta+b cos theta then prove that :x^(2)+y^(2)=a^(2)+b^(2)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, then a^(2)+b^(2)=m^(2)-n^(2)(b)m^(2)n^(2)(c)n^(2)-m^(2)(d)m^(2)+n^(2)

If a cos theat + b sin theta = m and a sin theta- b cos theta = n, then prove that a^2 + b^2 = m^2 + n^2

If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove that " x^(2)+y^(2)=a^(2)+b^(2).

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3) , then prove that m^(2)n^(2)(m^(2)+n^(2))=1.

If cosec theta- sin theta = m and sec theta - cos theta = n , prove that: (m^(2)n)^(2/3)+(n^(2)m)^(2/3)=1 .

If cos ec theta-sin theta=a^(3) and sec theta-cos theta=b^(3) then prove that a^(2)b^(2)(a^(2)+b^(2))=1