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 5)
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