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Trig Identities (Part 2)
The art of mastering all of the trigonometric identities is to be able to derive them by relying on the five identities [1]–[5] memorized in Part 1. You are expected to be able to derive each of the identities below, as you studied in trigonometry.
A complete process of deriving each of the identitles [8]–[24] is found in this handout.
The art of mastering all of the trigonometric identities is to be able to derive them by relying on the five identities [1]–[5] memorized in Part 1. You are expected to be able to derive each of the identities below, as you studied in trigonometry.
A complete process of deriving each of the identitles [8]–[24] is found in this handout.
| Pythagorean | How to Derive |
| [8] 1 + tan2(θ) = sec2(θ) | Divide both sides of [5] by cos2(θ). |
| [9] cot2(θ) + 1 = csc2(θ) | Divide both sides of [5] by sin2(θ). |
| Double-Angle | How to Derive |
| [10] sin(2θ) = 2sin(θ)cos(θ) | Let u = v = θ in [1]. |
| [11] cos(2θ) = cos2(θ) – sin2(θ) | Let u = v = θ in [2]. |
| [12] cos(2θ) = 2cos2(θ) – 1 | Use [5] to eliminate sin2(θ) in [11]. |
| [13] cos(2θ) = 1 – 2sin2(θ) | Use [5] to eliminate cos2(θ) in [11]. |
| Power-Reduction | How to Derive |
[14]  |
Solve [12] for cos2(θ). |
[15]  |
Solve [13] for sin2(θ). |
[16]  |
Divide [15] by [14]. |
Continue to Part 3.
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Disclaimer • Updated September 4, 2008
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Phone: +1 (610) 462-WPJW