# Prove that #(cscx)/(1+cscx)-(cscx)/(1-cscx)=2sec^2x#?

##### 4 Answers

You need to know that

#### Explanation:

I assume you meant:

These cosecant (

so let's change them since we know:

Let's transform our left-hand-side of the equation:

Let's first put everything under the same denominator:

and simplifying a bit, we get:

so

This then becomes

Again simplifying, we get:

We cancel the

Remember that there is this wonderful formula

and since

which is exactly the right-hand-side of the equation.

Q.E.D.

Please see below.

#### Explanation:

=

Multiplying each term by

=

=

=

=

Proved in the explanation.

#### Explanation:

Prove:

Multiply the left side of the equation by 1 in the form,

Please observe that, when the sine function is distributed, everywhere there was

Multiply the first term by 1 in the form

This makes the denominator become the difference of two squares:

Multiply the second term by 1 in the form

This makes the denominator become the same difference of two squares:

Put both numerators over the common denominator:

Combine like terms:

Substitute

Because

Q.E.D.

Make a common denominator.

#### Explanation:

Taking the left hand side & multiplying to get a common denominator,

=

=

=

( / is the divide symbol, easier to see when not in fraction form)

=

(Common denominator again by multiplying 1 by

=

(switch numerator & denominator and cancel out common terms)

=

=

(

=

=