Simplify without the use of calculater

Question

tan(360-x) x cos(x-180) x sin(90+x)÷cos(-x) x cos(360+x)

Answer 1

Mpumelelo,

I have used the following formulas to help simplify.

tan(a - b) = [ tan a - tan b] / [ 1 + (tan a)(tan b)]

cos(a - b) = (cos a)(cos b) + (sin a)(sin b)

cos(a + b) = (cos a)(cos b) - (sin a)(sin b)

sin(a + b) = (sin a)(cos b) + (cos a)(sin a)

tan(360-x) = [ tan 360 - tan x] / [ 1 + (tan 360)(tan x)] = [ 0 - tan x] / [ 1 + (0)(tan x)] = -tan x

cos(x-180) = (cos x)(cos 180) + (sin x)(sin 180) = (cos x)(-1) + (sin x)(0) = -cos x

sin(90+x) = (sin 90)(cos x) + (cos 90)(sin x) = (1)(cos x) + (0)(sin x) = cos x

cos(-x) = -cos x

cos(360+x) = (cos 360)(cos x) - (sin 360)(sin x) = (1)(cos x) - (0)(sin x) = cos x

Now I assume the math problem is as follows:

[(tan(360-x))(cos(x-180))(sin(90+x))] / [(cos(-x))(cos(360+x))]

= [(-tan x)(-cos x)(cos x)] / [(-cos(x))(cos x)]

= -tan x

Answer: -tan x