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Example Questions
Example Question #1 : Prove Trigonometric Identities
Simplify:
To simplify , find the common denominator and multiply the numerator accordingly.
The numerator is an identity.
Substitute the identity and simplify.
Example Question #1 : Prove Trigonometric Identities
Evaluate in terms of sines and cosines:
Convert into its sines and cosines.
Example Question #3 : Prove Trigonometric Identities
Simplify the following:
The expression is already in simplified form
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,
.
Example Question #1 : Prove Trigonometric Identities
Simplify the expression
To simplify, use the trigonometric identities and
to rewrite both halves of the expression:
Then combine using an exponent to simplify:
Example Question #1 : Prove Trigonometric Identities
Simplify .
This expression is a trigonometric identity:
Example Question #6 : Prove Trigonometric Identities
Simplify
Factor out 2 from the expression:
Then use the trigonometric identities and
to rewrite the fractions:
Finally, use the trigonometric identity to simplify:
Example Question #1 : Prove Trigonometric Identities
Simplify
Factor out the common from the expression:
Next, use the trigonometric identify to simplify:
Then use the identify to simplify further:
Example Question #8 : Prove Trigonometric Identities
Simplify
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:
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