Question

Prove the identity.

(1 - sin’x) cscx = cosx cotx
=
Note that each Statement must be based on
the right of the Rule.
rules:
algebra, reciprocal, quotient, pythagorean, odd/even

Answer 1

`\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\\ [1-sin^2(x)]csc(x)~~ = ~~cos(x)cot(x) \\\\[-0.35em] ~\dotfill\\\\\ [1-sin^2(x)]csc(x)\implies cos^2(x)csc(x)\implies cos^2(x)\cdot \cfrac{1}{sin(x)} \\\\\\ cos(x)\cdot \cfrac{cos(x)}{sin(x)}\implies cos(x)cot(x)`