Verify the identity 1 cos t1 cos t csc t cot t2 To verif

Verify the identity. 1 + cos t/1 - cos t = (csc t + cot t)^2 To verify the identity, start with the more complicated side and transform it to look like other side. Choose the correct transformation and transform the expression at each step. (csc t + cot t)^2 = (Do not simplify.) = (Simplify your answer.) = (Do not factor.0 = (Factor completely. Do not simplify.) = 1 + cos t/1 - cos t

Solution

(1-cost)/(1+ cos t)=(cosec t- cot t)²

(cosec t - cot t)²

cosec t= 1/ sin t and cot t= cos t/sin t

(1/sin t - cos t/sin t)²

We have to write that in the first fill in the blanks

((1-cos t)/sin t)²

we have to write ((1-cos t)/sin t)² in second fill in the blanks

(1-cos t)²/(sin t)²

And sin²t= 1 - cos²t

(1-cos t)²/(1-cos²t)

We have to write (1-cos t)²/(1-cos²t ) in the third fill in the blanks

factoring the numerator and denominator

(1-cos t)(1-cos t)/(1-cos t)(1+cos t) And we have to write (1-cos t)(1-cos t)/(1+cos t)(1-cos t) in last fill in the blanks