Write -5( tan(x) + sec(x)) ( 1 - sin(x)) in terms of sine and cosine.

Answer 1

First, a couple of things to note: tan x = sin x / cos x and sec x = 1/ cos x

With those things noted, we can rewrite the given equation in the following way:

-5(sin x / cos x + 1/ cos x)(1-sin(x))

= -5(sin x+1)/cos x)(1-sin x)

= -5(1+ sin x)/cos x * (1-sin x)

(a+b)*(a-b) = a² - b²

= -5(1-sin²x)/cos x

sin²x + cos ²x = 1 which implies cos²x = 1 - sin²x

= -5 cos² x /cos x

= -5 cos x