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Help verify each identity

(csc)/(cot \: x \: + \: tan \: x) = cos \: x

User Shrw
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1 Answer

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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


User Cashif Ilyas
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