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?

Expert Answers

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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