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Use the Pythagorean identity to do the following:
a. Rewrite the expression cos(theta) sin2(theta) − cos(theta) in terms of a single trigonometric function. State the resulting
identity.

Respuesta :

Answer:  2 - 2*sin³(θ) - √1 -sin²(θ)

Step-by-step explanation:  In the expression

cos(theta)*sin2(theta) − cos(theta)

sin (2θ) = 2 sin(θ)*cos(θ)     ⇒   cos(θ)*2sin(θ)cos(θ) - cos(θ)

2cos²(θ)sin(θ) - cos(θ)           if we use cos²(θ) = 1-sin²(θ)

2 [ (1 - sin²(θ))*sin(θ)] - cos(θ)

2  - 2sin²(θ)sin(θ) - cos(θ)  ⇒  2-2sin³(θ)-cos(θ)   ;  cos(θ) = √1 -sin²(θ)

2 - 2*sin³(θ) - √1 -sin²(θ)

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