Question

Help verify each identity%3A%20tan%20%5C%3A%20x%7D%20%20%3D%20cos%20%5C%3A%20x" id="TexFormula1" title=" \frac{csc}{cot \: x \: + \: tan \: x} = cos \: x" alt=" \frac{csc}{cot \: x \: + \: tan \: x} = cos \: x" align="absmiddle" class="latex-formula">

Answer 1

cot x = cos x / sin x

tan x = sin x / cos x

(Find common denominators)

cosx/sinx * cosx/cosx = cos^2x/sinxcosx

sinx/cosx * sinx/sinx = sin^2x/sinxcosx

(Now we can combine them)

csc / (sin^2x+cos^2x / sinxcosx)

(Simplify)

csc*sinx*cosx / sin^2x+cos^2x

sin^2x + cos^2x = 1

csc*sinx*cosx / (1)

csc*sinx*cosx

csc = 1/sinx

1/sinx*sinx = 1

(1)*cosx = cosx