(tan alpha+cot alpha)/(sin alpha-cos alpha)=sec^2 alpha+csc^2 alpha

Alyce Wilkinson 2021-09-04 Answered

tanα+cotαsinαcosα=sec2α+csc2α

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Expert Answer

Benedict
Answered 2021-09-05 Author has 108 answers

Work on the left side. Separate as:

Work on the left side.
Separate as:
tanα+cotαsinαcosα=(tanαsinαcosα+(cotαsinαcosα))
Use the quotient identity for tangent and cotangent:
tanα+cosαsinαcosα=((sinαcosαsinαcosα)+(cosαsinαsinαcosα))
Simplify:
(tanα+cotαsinαcosα)=1cos2α+1sin2α
Use the reciprocal identities for cosine and sine:
tanα+cotαsinαcosα=sec2α+csc2α

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