Question

Prove (sinx + sin2x) / (1+cosx + cos2x) = tanx

Answer 1

By sin2x and tan2x you mean \(\sin^2x\) and \(\tan^2 x\) or \(\sin (2x)\) and \(\tan (2x)\)?

Answer 2

sin(2x) and cos(2x)

Answer 3

\(\bf \cfrac{sin(x)+sin(2x)}{1+cos(x)+cos(2x)}\\ \quad \\
\textit{recall that }sin(2x)=2sin(x)cos(x)\qquad cos(2x)=2cos^2(x)-1\\ \quad \\

\cfrac{sin(x)+sin(2x)}{1+cos(x)+cos(2x)}\implies \cfrac{sin(x)+2sin(x)cos(x)}{\cancel{1}+cos(x)+2cos^2(x)\cancel{-1}}\)

now, take common factors atop and bottom, see what you get

Answer 4

Ohhh got it thanks :)

Answer 5

yw