How to show that 1+tan²(θ)=sec²(θ) and 1+cot²(θ)=cosec²(θ)

In the workings below I demonstrate how you can derive 1+tan²(θ)=sec²(θ) and 1+cot²(θ)=cosec²(θ) using sin²(θ)+cos²(θ)=1.

 
Just follow the instructions, and presto!

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