What is cottheta-csctheta-costhetacotθ−cscθ−cosθ in terms of sinthetasinθ?

1 Answer
Johnson Z.
Dec 9, 2015

(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@cosθ−cosθsinθ−1sinθ,θ≠0∘,180∘,360∘

Explanation:

Recall:
1. cotx=1/tanx1.cotx=1tanx or cosx/sinxcosxsinx
2. cscx=1/sinx2.cscx=1sinx

Substitute your reciprocal and quotient identities into the equation:

cottheta-csctheta-costhetacotθ−cscθ−cosθ

=costheta/sintheta-1/sintheta-costheta=cosθsinθ−1sinθ−cosθ

=(costheta-1-costheta(sintheta))/sintheta=cosθ−1−cosθ(sinθ)sinθ

=(costheta-1-costhetasintheta)/sintheta=cosθ−1−cosθsinθsinθ

=(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@=cosθ−cosθsinθ−1sinθ,θ≠0∘,180∘,360∘

Related questions
See all questions in Fundamental Identities
Impact of this question
1717 views around the world
You can reuse this answer
Creative Commons License