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Trigonometric Identities

Problems

Additional Trigonometric Identities

Review of Functions and Angles

Problem : Prove the following identity: tan(θ)cos(θ) = sin(θ)

tan(θ)cos(θ) = sin(θ)    

= sin(θ)    

sin(θ) = sin(θ)    

Problem : Prove the following identity: (sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = tan(θ)cot(θ)

(sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = tan(θ)cot(θ)    

(sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 =    

(sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = 1    

((sin(θ))2 + (cos(θ))2)((sin(θ))2 + (cos(θ))2) = 1    

(1)(1) = 1    

Problem : Prove the following identity: - cos(θ)(cot(θ))2 = cot(θ)sin(θ)

- cos(θ)(cot(θ))2 = cot(θ)sin(θ)    

- =    

- = cos(θ)    

- = 1    

(csc(θ))2 - (cot(θ))2 = 1    

(csc(θ))2 = 1 + (cot(θ))2    

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