Question #3d30a

1 Answer
Jun 24, 2017

Multiply both sides by sin(x)cos(x).

Explanation:

Here is how you can prove the identity is true. First, express all terms as either sin(x) or cos(x)

(1/sin(x)+1/cos(x))/(sin(x)+cos(x))=cos(x)/sin(x)+sin(x)/cos(x)

Then multiply both sides by sin(x)cos(x)

sin(x)cos(x)xx(1/sin(x)+1/cos(x))/(sin(x)+cos(x))
=sin(x)cos(x)xx(cos(x)/sin(x)+sin(x)/cos(x))

The left hand side multiplies sin(x)cos(x) through the numerator, giving

(cos(x)+sin(x))/(sin(x)+cos(x))=1

The right hand side multiplies sin(x)cos(x) though each term, giving

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

Because the left hand side equals the right hand side, the identity is proven.