Asked by Anna
What is the simplified for of the expression cos theta / csc theta - sin theta?
How do you show your work on this?
How do you show your work on this?
Answers
Answered by
oobleck
since cscθ = 1/sinθ,
cosθ/cscθ - sinθ
= cosθ sinθ - sinθ
= sinθ(cosθ-1)
or maybe you meant
cosθ/(cscθ-sinθ)
= cosθ/(1/sinθ - sinθ)
= cosθ sinθ / (1 - sin^2θ)
= cosθ sinθ / cos^2θ
= sinθ/cosθ
= tanθ
parentheses can make a difference!
cosθ/cscθ - sinθ
= cosθ sinθ - sinθ
= sinθ(cosθ-1)
or maybe you meant
cosθ/(cscθ-sinθ)
= cosθ/(1/sinθ - sinθ)
= cosθ sinθ / (1 - sin^2θ)
= cosθ sinθ / cos^2θ
= sinθ/cosθ
= tanθ
parentheses can make a difference!
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