# Answer to Question #751 in Trigonometry for Amaan

Question #751

Write in terms of sin and cos and simplify.

cot(theta)/(csc(theta)-sin(theta))

cot(theta)/(csc(theta)-sin(theta))

Expert's answer

Cot (θ)/csc(θ)-sin(θ)=(cos(θ)/sin(θ))/(1/sin(θ))-sin(θ)=

=(cos(θ)/sin(θ))/(1-sin2(θ))/sin(θ)=

=(cos(θ)/sin(θ))/(cos2(θ)/sin(θ))=

=(sin(θ)cos(θ))/(sin(θ)cos2(θ))=

=1/cos(θ)=sec(θ)

=(cos(θ)/sin(θ))/(1-sin2(θ))/sin(θ)=

=(cos(θ)/sin(θ))/(cos2(θ)/sin(θ))=

=(sin(θ)cos(θ))/(sin(θ)cos2(θ))=

=1/cos(θ)=sec(θ)

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