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education/math/MATH1060 (trig)/Identities.md
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An **identity** is an equation that is true for all values of the variable for which the expressions in the equation are defined.
# Trigonometric Identities # Trigonometric Identities
All of the following only apply when the denominator is not equal to zero. All of the following only apply when the denominator is not equal to zero.
@ -63,4 +64,12 @@ $$ \frac{625}{625} - \frac{49}{625} = \frac{576}{625} = sin^2\theta $$
Getting rid of the exponent: Getting rid of the exponent:
$$ \sqrt{\frac{576}{625}} = \frac{24}{25} = sin\theta $$ $$ \sqrt{\frac{576}{625}} = \frac{24}{25} = sin\theta $$
From there, you can find the rest of the identities fairly easily. From there, you can find the rest of the identities fairly easily.
# Simplifying trig expressions using identities
Given the difference of square formula:
$$ a^2 - b^2 = (a-b)(a+b) $$
## Examples
Simplify $\tan\theta\sin\theta + \cos\theta$:
1. $\frac{\tan\theta\sin\theta}{\sin\theta} + \frac{cos\theta}\frac{sin\}