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- Trigonometric Identities

Still Confused?

Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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Trig identities are formulas developed based on Pythagorean Theorem. These identities show us how and where to find the sine, cosine, and tangent of the sum and difference of two given angles.

Basic concepts: Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ ), Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ ), Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ ), Trigonometric ratios of angles in radians,

Related concepts: Solving trigonometric equations using sum and difference identities,

Download the Trigonometry identities chart here

Formulas:$\sin (A + B)$

$\sin (A - B)$

$\cos (A + B)$

$\cos (A - B)$

$\tan (A + B)$

$\tan (A - B)$

Formulas:$\sin (A + B)$

$\sin (A - B)$

$\cos (A + B)$

$\cos (A - B)$

$\tan (A + B)$

$\tan (A - B)$

- 1.Simplify expressionsa)sin 24°cos 36° + cos 24°sin 36°

b)$\frac{tan {2 \pi \over 5 } - tan {3 \pi \over 20}}{1 + \tan {2 \pi \over 5} \cdot \tan {3 \pi \over 20}}$ - 2.Prove Identitiesa)$\frac{\sin (A - B)}{\sin B} + \frac{\cos (A - B)}{\cos B} = \frac{\sin A}{\sin B \cos B}$b)$\frac{1 + \tan A}{\tan (A + {\pi \over 4})} = 1 - \tan A$
- 3.Without using a calculator, evaluate:a)sin 15°b)sec (-105°)c)$tan {19\pi \over 12}$
- 4.Given $\sin A = -{4 \over5}$ and $\cos B = {12 \over 13} ,$

where $\pi \leq A \leq {3 \pi \over 2}$ and ${3 \pi \over 2} \leq B \leq 2\pi ,$

find the exact value of $\cos (A + B)$

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