Trigonometry · Chapter 6 of 11

Compound & multiple angles

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The cosine of a sum or difference of two angles is found using $cos (A \pm B) = cos A cos B \mp sin A sin B$ . These identities let you evaluate trigonometric functions for angles built from standard angles such as $3 0^{\circ}$ , $4 5^{\circ}$ , and $6 0^{\circ}$ . Repeated use of the sum formulas also produces multiple-angle formulas, such as $cos 3 θ = 4 cos^{3} θ - 3 cos θ$ .

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#	Title	Difficulty	Tags
74	The triple angle	Medium	Angle additionDouble angle

From open sources

Complete problems only, with worked solutions first. Show everything

#	Title	Difficulty
103898	Sum and Difference Identities · Exercise 21	Medium
103912	Sum and Difference Identities · Exercise 35	Medium
103916	Sum and Difference Identities · Exercise 39	Medium
103918	Sum and Difference Identities · Exercise 41	Medium
103920	Sum and Difference Identities · Exercise 43	Medium
103951	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 5	Medium
103955	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 9	Medium
103967	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 21	Medium
103969	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 23	Medium
103973	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 27	Medium
103981	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 35	Medium
103983	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 37	Medium
103987	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 41	Medium
103989	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 43	Medium
103991	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 45	Medium
103995	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 49	Medium
104026	Sum-to-Product and Product-to-Sum Formulas · Exercise 5	Medium
104030	Sum-to-Product and Product-to-Sum Formulas · Exercise 9	Medium
104045	Sum-to-Product and Product-to-Sum Formulas · Exercise 25	Medium
104053	Sum-to-Product and Product-to-Sum Formulas · Exercise 33	Medium
104055	Sum-to-Product and Product-to-Sum Formulas · Exercise 35	Medium
104057	Sum-to-Product and Product-to-Sum Formulas · Exercise 37	Medium
104059	Sum-to-Product and Product-to-Sum Formulas · Exercise 39	Medium
104063	Sum-to-Product and Product-to-Sum Formulas · Exercise 43	Medium
107361	Sum and Difference Identities · Exercise 43	Medium
107371	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 9	Medium
107378	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 35	Medium
107380	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 37	Medium
107392	Sum-to-Product and Product-to-Sum Formulas · Exercise 39	Medium
107394	Sum-to-Product and Product-to-Sum Formulas · Exercise 41	Medium
107396	Sum-to-Product and Product-to-Sum Formulas · Exercise 43	Medium
103882	Sum and Difference Identities · Exercise 5	Medium
103884	Sum and Difference Identities · Exercise 7	Medium
103886	Sum and Difference Identities · Exercise 9	Medium
103888	Sum and Difference Identities · Exercise 11	Medium
103890	Sum and Difference Identities · Exercise 13	Medium
103892	Sum and Difference Identities · Exercise 15	Medium
103894	Sum and Difference Identities · Exercise 17	Medium
103896	Sum and Difference Identities · Exercise 19	Medium
103900	Sum and Difference Identities · Exercise 23	Medium
103910	Sum and Difference Identities · Exercise 33	Medium
103914	Sum and Difference Identities · Exercise 37	Medium
103922	Sum and Difference Identities · Exercise 45	Medium
103953	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 7	Medium
103957	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 11	Medium
103959	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 13	Medium
103961	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 15	Medium
103963	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 17	Medium
103965	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 19	Medium
103971	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 25	Medium