Verifying Trigonometric Indentities

Question

1+cost/ 1- cost t= (csc t+ cot t)^2

(csc t + cot t)^2=

Answer 1

Here is a Desmos graph showing that the graph of the left side is the same as the graph of the right side.

desmos.com/calculator/sjk96o4tbp

Answer 2

(1+cos(t))/(1-cos(t)) =((1+cos(t))/(1-cos(t))) (1+cos(t)/(1+cos(t)) = (1+cos(t))²/(1-cos²(t))

= (1+2cos(t)+cos²(t))/sin²(t) =csc²(t)+2csc(t)cot(t)+cot²(t)

= (csc(t)+cot(t))²