Trigonometry - Trigonometric identities.
Test Yourself 1 - Solutions.
Simplify the following trigonometric identities:
Basic substitutions. | 1. ![]() |
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Complementary angles. | 9.
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Pythagorean relationships. | 11. ![]() |
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Prove the following trigonometric identities:
Basic substitutions (change of defintion). |
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18. sec2 x - tan2 x = 1
LHS = 1 + tan2x - tan2x = 1 = RHS |
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Complementary angles. | 19.
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Pythagorean relationships. | 21. (1 - sin θ)(1 + sin θ) = cos 2θ
LHS = 1 - sin2θ = cos2θ = RHS |
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23. sin4 x + cos2sin2x = sin2 x LHS = sin2x(sin2x + cos2x) =sin2x = RHS |
24. sec β - cos β = sin β tan β![]() |
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27. 3sin2 A + 2 cos2 A = sin2 A + 2 LHS = sin2 A +(2sin2 A +2cos2 A) = sin2 A + 2 = RHS |
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35. LHS = (sin B + cos B)2 + (sin B - cos B)2 = sin2 B + 2sin Bcos B + cos2 B + sin2 B - 2sin B cos B + cos2 B = 2sin2 B + 2 cos2 B = 2(sin2 B + cos2 B) = 2 = RHS |