In the following equation, what is the value of x, within 0<x<360 : cos(x)tan(x) - 2cos(x) + tan(x) - 2 = 0 and what are the steps to simplifying the equation?
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cos(x)tan(x) - 2cos(x) + tan(x) - 2 = 0
The first step is to 'group' them such that you can simplify them into two sets:
[cos x tan x + tan x] + [- 2 cos x - 2] = 0
Now simplify each set. Take care with the (-) as it changes the symbol:
tan x(cos x + 1) - 2(cos x + 1) = 0.The common factor is now (cosx+1) so simplify
(cos x + 1)(tanx - 2) = 0. Each factor =0 and so solve each one:
(cos x + 1) = 0
`:.` cos x = -1
`:.` x= 180 degrees + k.360 degrees within the domain 0<x<360
x= 180 degrees k (element of Z)
(tan x - 2) = 0
tan x = 2
x= 63, 43 degrees + k.360 degrees
x= 63,43 degrees k(element of` Z` )
x= 180 degrees
x= 63,43 degrees
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