Prove Trigonometric Identities - Pre-Calculus

First factor out sine x.

Notice that a Pythagorean Identity is present.

The identity needed for this problem is:

Using this identity the equation becomes,

.

Convert into its sines and cosines.

To simplify, use the trigonometric identities and to rewrite both halves of the expression:

Then combine using an exponent to simplify:

This expression is a trigonometric identity:

Factor out 2 from the expression:

Then use the trigonometric identities and to rewrite the fractions:

Finally, use the trigonometric identity to simplify:

Factor out the common from the expression:

Next, use the trigonometric identify to simplify:

Then use the identify to simplify further:

To simplify the expression, separate the fraction into two parts:

The terms in the first fraction cancel leaving you with:

Then you can deal with the remaining fraction using the rule that . This leaves:

You can separate this into:

And each half of this expression is now a trigonometric identity: and . This gives you:

To simplify , find the common denominator and multiply the numerator accordingly.

The numerator is an identity.

Substitute the identity and simplify.

First factor out sine x.

Notice that a Pythagorean Identity is present.

The identity needed for this problem is:

Using this identity the equation becomes,

.

Convert into its sines and cosines.

To simplify, use the trigonometric identities and to rewrite both halves of the expression:

Then combine using an exponent to simplify:

This expression is a trigonometric identity:

Factor out 2 from the expression:

Then use the trigonometric identities and to rewrite the fractions:

Finally, use the trigonometric identity to simplify:

Factor out the common from the expression:

Next, use the trigonometric identify to simplify:

Then use the identify to simplify further:

To simplify the expression, separate the fraction into two parts:

The terms in the first fraction cancel leaving you with:

Then you can deal with the remaining fraction using the rule that . This leaves:

You can separate this into:

And each half of this expression is now a trigonometric identity: and . This gives you:

To simplify , find the common denominator and multiply the numerator accordingly.

The numerator is an identity.

Substitute the identity and simplify.

First factor out sine x.

Notice that a Pythagorean Identity is present.

The identity needed for this problem is:

Using this identity the equation becomes,

.

Convert into its sines and cosines.

To simplify, use the trigonometric identities and to rewrite both halves of the expression:

Then combine using an exponent to simplify: