prove the trigonometric identity

Question

(1-cos^2x)(cot^2+1) = 1

Answer 1

(1-cos²θ)(cot²θ+1)

 

use the identities: sin²θ= 1-cos²θ   and   cot²θ + 1 = csc²θ

 

(sin²θ)(csc²θ)

 

now cscθ = 1/sinθ

 

(sin²θ)(1/sin²θ)

 

1