Question

Simplify
sec x - tan x sin x
a) cos x
b) cot x
c) 1-csc x
d) csc x

Answer 1

cos x is the answer.

Explanation:

secx - tanx sinx

`(1)/(cosx) - (sinx)/(cosx) * sinx\\\\(1)/(cosx) - (sin^(2)x)/(cosx)\\\\(1-sin^(2)x)/(cosx) \\\\(cos^(2)x )/(cosx) \\\\cosx`