Question #b5658

1 Answer
May 25, 2017

See Below.

Explanation:

Identities Required:
sin(2x)=2sin(x)cos(x)

sin^2(x)+cos^2(x)=1
sin^2(x)=1-cos^2(x)

cos(2x)=cos^2(x)-sin^2(x) =cos^2(x)-(1-cos^2(x))=2cos^2(x)-1

Now solving:
sin(2x)/sin(x)-cos(2x)/cos(x)=sec(x)
(2sin(x)cos(x))/sin(x)-(2cos^2(x)-1)/cos(x)=RHS
2cos(x)-2cos(x)+1/cos(x)=RHS
sec(x)=RHS
QED