Question

Evaluate: tan^2(x) - 3tan(x) + 2 = 0

Answer 1

x= 63.43° and x= 45°

Explanation:

Given that

`tan^2x-3 tanx +2=0`

Lets assume that

tan x =k

Now by replace tan x by k we will get

`k^2-3 k +2=0`

Now above equation is a quadratic equation

`k^2-2 k - k+2=0`

k(k-2)-1(k-2)=0

So k=2,k=1

Now putting tan x in place of k

tan x =2 and tan x =1

So by using inverse property

x= 63.43°

tan x =1

x= 45°

Answer 2

Let u be the value of tan(x) and that the equation above may also be written as,
u² - 3u + 2 = 0
The equation can be factored as follows,
(u - 1)(u - 2) = 0
u - 1 = 0 ; u = 1 and u - 2 = 0 ; u = 2
Thus, tangent(x) = 1 and tangent(x) = 2. The values of x are 45° and 63.43°.