Question

Question #49d56

Answer 1

see explanation

Explanation:

let's take the left hand side (abbr. LHS) to prove the right hand side (abbr. RHS)...

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`(csc x - sin x)/cos x`

`= \color(indianred)((1/sin x) -sin x)/cos x = \color(indianred)((1 - sin^2 x)/sin x)\times1/cos x`

`= (1 - sin^2 x)/(sin x cos x) = cos^cancel(2)x/(sin x cancelcos x)`

`= cos x/sin x = cot x` `\color(green)(\sqrt())`