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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How to derive tan(π/8), sin(π/8) and cos(π/8) from scratch
Below I demonstrate how to derive tan(π/8) , sin(π/8) and cos(π/8) from scratch. These workings are a bit similar to the workings for tan((3π)/8) , sin((3π)/8) and cos((3π)/8) which can be found here : https://geometricbites.blogspot.com/2021/08/how-to-derive-tan38-sin38-and-cos38.html The edge with length R √(2- √(2)) was actually derived in the tan((3π)/8), sin((3π)/8) and cos((3π)/8) post, so doesn't need to be found again. Part 1 Part 2 Part 3 Part 4
How to derive tan((3π)/8), sin((3π)/8) and cos((3π)/8) from scratch (geometric + algebraic)
Below I demonstrate how to derive tan((3π)/8) , sin((3π)/8) and cos((3π)/8) from scratch. I use geometry and also algebra . Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 If you'd like quick updates every time I post, follow me on Twitter at: https://twitter.com/tiago_hands .