Trigonometric Identities: Problems 2

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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