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
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)
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)
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)