Question

Prove that tanx-cotx/sinx cosx = tan^2x-cot^2x

Answer 1

tanx-cotx/sinxcosx
=(sinx/cosx-cosx/sinx)/sinxcosx
={(sin²x-cos²x)/sinxcosx}/sinxcosx
=(sin²x-cos²x)/sin²xcos²x
=1/cos²x-1/sin²x
=sec²x-cosec²x
=1+tan²x-(1+cot²x) [∵, sec²x-tan²x=1 and cosec²x-cot²x=1]
=tan²x-cot²x (Proved)