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

Question

How do u proof that LHS=RHS

Answer 1

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)

Answer 2

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