Question

how to simplify cos(2w)/cos(w)+sin(w)

Answer 1

\(\bf \cfrac{cos(2w)}{cos(w)+sin(w)}\quad ?\)

Answer 2

yes how to simplify using trig identities

Answer 3

http://www.mathwords.com/t/trig_identities.htm <--- look at the double-angle identities

Answer 4

\(\bf \cfrac{cos(2w)}{cos(w)+sin(w)}\\ \quad \\ \quad \\
\textit{notice that }\quad \color{blue}{cos(2\theta)=cos^2(\theta)-sin^2(\theta)}\qquad thus\\ \quad \\

\cfrac{cos(2w)}{cos(w)+sin(w)}\implies \cfrac{cos^2(w)-sin^2(w)}{cos(w)+sin(w)}\\ \quad \\
\textit{now recall that }\quad \color{blue}{a^2-b^2 = (a-b)(a+b)}\qquad thus\\ \quad \\

\cfrac{cos^2(w)-sin^2(w)}{cos(w)+sin(w)}\implies \cfrac{[cos(w)-sin(w)][cos(w)+sin(w)]}{cos(w)+sin(w)}\)

Answer 5

and you can see what cancels out there

Answer 6

thank you thank you thank you!!!!

Answer 7

yw