Solve the equation 3 tan x - 4 - sec x = 0.

Expert Answers

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You need to replace `tan x = sin x/cos x and sec x = 1/cos x`

`3sin x/cos x - 4 - 1/cos x = 0`

You need to bring the terms to a common denominator:

`(3sin x - 4cos x - 1)/cos x = 0=gt 3sin x - 4cos x - 1 = 0`

`3sin x - 4cos x= 1`

`` You should come up with the following substitutions:

`sin x = 2tan(x/2)/(1 + tan^2(x/2)); cos x = (1- tan^2(x/2))/(1 + tan^2(x/2))`

`` `(6tan(x/2) - 4 + 4tan^2(x/2) - 1 - tan^2(x/2))/(1 + tan^2(x/2)) = 0`

`3tan^2(x/2) +6tan(x/2) - 5 = 0`

`tan(x/2) = (-1+sqrt(36 + 60))/6=gttan(x/2)=1.46 =gt x/2~~56^o =gt x ~~ 112^o`

The solution to the given equation is x`~~ 112^o` .

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