Question

Verify the identity and show all steps.

Answer 1

\[(\tan(x)-\cot(x))\div(\tan ^{2}(x)-\cot ^{2}(x))=\sin(x)\cot(x)\]

Answer 2

LHS = (tanx - cotx) divided by (tanx - cotx)(tanx + cotx)

= 1/(tanx + cotx)

= 1/((sinx/cosx) + (cosx/sinx))

= 1/(((sinx)^2 + (cosx)^2)/sinxcosx)

= sinxcosx/1

= sinxcosx