Trigonometric Identities

Presented byPaula Almiron

Thea DeGuzmanRaashmi Patalapati

The Trigonometric Identities

Memorize them. Use them. Love them.

Tips for Solving Trigonometric Expressions and Identities

• USE THE TRIGONOMETRIC IDENTITIES

• Factor factor factor!• Look for common denominators• Multiply by 1 (or some other form of

it)

Simplifying Expressions

tan2 x cos2 x + cot2 x sin2 x

Practice Problem #1

Start by looking for any identities you may be able to use.

tan2 x cos2 x + cot2 x sin2 x

Using the quotient identities, we can break down the whole expression into

sines and cosines.

sin2 x/cos2 x (cos2 x) + (cos2 x/sin2 x) (sin2 x)

Now, we multiply both expressions by the term in parentheses. We can

eliminate the denominator of both expressions.

sin2 x/cos2 x (cos2 x) + (cos2 x/sin2 x) (sin2 x)

sin2 x + cos2 x = 1

Then, by using the Pythagorean identity of sines and cosines, we

simplify the expression down to 1.

Verifying Identities

Practice Problem #2

Always start with the more complicated side and try to break it

down into simpler terms. In this case, we will start with the left side.

Do not, under any circumstances, work on both sides of the equation. This is expressly forbidden by the

Laws of Trigonometry.

Practice Problem #1

Using the quotient identities, rewrite the left side of the equation. Thus, our

equation only consists of sines and cosines, the same as the right side.

Simplify the expression.

Here, we multiply by one in order to give the equation in brackets a

common denominator.

Add the two expressions within the brackets.

Multiply out the equation by the expression outside the brackets.

All done!