Answer
See below.
Work Step by Step
The identity is equivalent to $(csc\theta+cot\theta)(csc\theta-cot\theta)=(sec\theta+tan\theta)(sec\theta-tan\theta)\longrightarrow csc^2\theta-cot^2\theta=sec^2\theta-tan^2\theta \longrightarrow 1=1$ Which is true.