Trigonometric Identities

In this tutorial the students learn how to use trigonometric identities and properties of trigonometry to prove that trigonometric expressions are equal.

Virginia Standards of Learning(SOL) T.5

Key Skills

Trigonometric Identities

1/cos(x) = sec(x)

1/sin(x) = csc(x)

tan(x) = sin(x)/cos(x)

1/tan(x) = cos(x)/sin(x)

1/tan(x) = cot(x)

Pythagorean Identities

sin²x + cos²x = 1

1 + cot²x = csc²x

tan²x + 1 = sec²x

Sine Double Angle Identity

sin(2x) = 2sin(x)cos(x)

Cosine Double Angle Identity

cos(2x) = cos²(x) - sin²(x)

Conjugate

A binomial where the second term is negated.

(x + 2) conjugate (x - 2)

(1 - cos x) conjugate (1 + cos x)

Difference of Perfect Squares

The subtraction of 2 perfect squares can be factored into what you see below.

(a² - b²) = (a + b) (a - b)

More examples

• Trigonometric Identity (Example 1)

• Double Angle Identity (Sine)

• Double Angle Identity (Cosine)

• Trigonometric Identity (Example 3)

• Trigonometric Identity (Example 2)

• Trigonometric Identity (Example 4)

• Trigonometric Identity (Example 6)

The key to solving these types of problems is making substitutions and knowing your basic trigonometric identities.