Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

# Sin2x/(sinx) - cos2x/(cos x)?

How do u proof that LHS=RHS

### 2 Answers

Relevance
• Favorite Answer

Since cos^2(x)=(1+cos2x)/2 so we obtain cos2x=2cos^(x)-1 also we know sin2x=2sin(x)cos(x) now if we put these things in what u have writen we will have [(2sin(x)cos(x)]/sin(x) - (2cos^(x)-1)/cos(x) = 2cos(x)-2cos(x)+ (1/cos(x))=sec(x)

Source(s): Me
• Only one side of equation is given

any how you can simplify this as follows

sin 2x / sin x - cos 2x / cos x

Taking LCM we get

(sin2x cosx - cos 2x sin x) /sin x cos x

sin(2x -x) / sinx cos x using Sin (A-B) sinAcosB - cosAsinB

sin x/ sin x cos x = 1/cos x

sec x

Still have questions? Get your answers by asking now.