Question

Question #3d30a

Answer 1

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.