Verifying Trig Equations \frac{\tan x}{1-\cos x} = \csc x(1+\sec x) I have

Sullivan Pearson

Sullivan Pearson

Answered question

2022-04-20

Verifying Trig Equations
tanx1cosx=cscx(1+secx)
I have spent a few hours trying to simplify the left side but I can't seem to find the solution. I would appreciate a pointing in the right direction.

Answer & Explanation

bobthemightyafm

bobthemightyafm

Beginner2022-04-21Added 16 answers

tanx1cosx=tanx1cosx×1+cosx1+cosx
=tanx(1+cosx)1cos2xsin2x
=(sinxcosx)(1+cosxsin2x)
=(sinxsin2x)(1+cosxcosx)Swapping of denominators
=(1sinx)(1+cosxcosx)
=cscx(1+secx)

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