How do you simplify the expression (1+costheta)(csctheta-cottheta)(1+cosθ)(cscθ−cotθ)?

1 Answer
Salvatore I.
Nov 6, 2016

sin(theta)sin(θ)

Explanation:

It ca be rewritten as
(1+cos(theta))(1/sin(theta)-cos(theta)/sin(theta))(1+cos(θ))(1sin(θ)−cos(θ)sin(θ))

that becomes

(1+cos(theta))(1-cos(theta))/sin(theta)=(1-cos^2(theta))/sin(theta)=sin^2(theta)/sin(theta)=sin(theta)(1+cos(θ))1−cos(θ)sin(θ)=1−cos2(θ)sin(θ)=sin2(θ)sin(θ)=sin(θ)

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