tanx+cotx/sec^2x=cotx

Question

how do you verify this

Answer 1

Start with the trig identity sec^2= 1+tan^2

(tan +cot)/(1+tan^2)= cot

tan +cot = ( 1 + tan^2 )(cot). Distribute

tan + cot = cot +(cot)tan^2. Cot=1/tan

tan + cot = cot + (1/tan)(tan^2

tan + cot = cot +tan

There you go