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If acostheta+bsintheta=ma n dasintheta-b...

If `acostheta+bsintheta=ma n dasintheta-bcostheta=n ,` Prove that `a^2+b^2=m^2+n^2`

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i) If acostheta+bsintheta=m and asintheta-bcostheta=n , then prove that: a^(2)+b^(2)=m^(2)+n^(2)

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)

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If x=acostheta-bsinthetaandy=asintheta+bcostheta , then show that : x^(2)+y^(2)=a^(2)+b^(2)

If acostheta+bsintheta=c , then prove that: asintheta-bcostheta=+-sqrt(a^(2)+b^(2)-c^(2))

If x=acostheta+bsintheta,y=asintheta-bcostheta , show : y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0 .

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If acostheta-bsintheta=c , then prove that: asintheta+bcostheta=+-sqrt(a^(2)+b^(2)-c^(2))