If $a \cos heta + b \sin heta = m$ and $a \sin heta - b \cos heta = n$, then prove that $a^2 + b^2 = m^2 + n^2$.

Question

If $a \cos 	heta + b \sin 	heta = m$ and $a \sin 	heta - b \cos 	heta = n$, then prove that $a^2 + b^2 = m^2 + n^2$.

Accepted Answer

Step 1: $m^2 + n^2 = (a \cos 	heta + b \sin 	heta)^2 + (a \sin 	heta - b \cos 	heta)^2$
Step 2: $= a^2(\cos^2 	heta + \sin^2 	heta) + b^2(\sin^2 	heta + \cos^2 	heta)$
Step 3: $= a^2 + b^2$

Question

Solution