Question

Using trig identities, prove the equation shown below.

sec(x) – sin(x)tan(x) = cosx

Hint: Work on the left side of the equation and do not manipulate the right side of the equation.

Answer 1

Explanation:

Prove that

sec(x) - sin(x)tan(x)=cosx

sec(x)=1/cos(x) tan(x)=sin(x)/cos(x)

1/cos(x) - sin(x) x sin(x)/cos(x)

(1-sin(x) x sin(x))/cos(x)

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

Cos^2(x)/cos(x)

(Cos(x) x cos(x))/cos(x)

cos(x) proved