Given $\tan \theta =b/a$, then find $a\cos2\theta+b\sin2\theta$ in terms of $a$ and $b$.
I tried to solve the problem by first converting $\sin2\theta$ and $\cos2\theta$ in the $\tan$ terms (applying formula) and then simplifying it. But I did not get the correct answer, which is $a$.
Then I tried to substituting like this
$$a\cos2\theta + \tan\theta\sin2\theta.$$
I got a quadratic equation which I solved and substituted the values but failed to get the correct answer.
Best Answer
Hint
You could use the tangent half-angle substitution (Weierstrass substitution). Using $t=\tan(\theta)$, you have $$\sin(2\theta)=\frac{2 t}{1+t^2}$$ $$\cos(2\theta)=\frac{1-t^2}{1+t^2}$$
I am sure that you can take from here.