Evaluating a Trigonometric Expression InExercises 47–52, find the exact value of the trigonometricexpression given that sin u = − 725 and cos v = −45. (Bothu and v are in Quadrant III.)47. cos(u + v) 48. sin(u + v)49. tan(u − v) 50. cot(v − u)51. csc(u − v) 52. sec(v − u)

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A: We need to compute the trigonometric ratios for the given triangle.

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A: Method 1÷

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A: 15. To write: cos 4θ in terms of cos θ and sin θ.

Q: Establish each identity.

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Q: Establish each identity.

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.