Question

please help me with this trig problem

Answer 1

any problem ask in comment section.

Answer 2

let us replace Theta by x. acosx+bsinx=3=> on squaring On both sides we get a^2cosx^2+ b^2sinx^2+2(acosx)(bsinx)=9...(1) . asinx-bcosx=4on squaring this equation on both sides we get=>a^2sinx^2+b^2cosx^2-2(asinx)(bcosx)=16...(2)
Add equations(1)and (2) we get a^2(sinx^2+cosx^2)
+b(cosx^2+sinx^2)+2absinxcosx-2absinxcosx=16+9
=> a^2+b^2=25. as sinx^2+cosx^2=1 .So (A)is the answer.