SOLUTION: Sin x tan x - sin x + tan x - 1=0 find value of x if x belongs to [0,2π]

Algebra ->  Trigonometry-basics -> SOLUTION: Sin x tan x - sin x + tan x - 1=0 find value of x if x belongs to [0,2π]       Log On


   

Question 1062943: Sin x tan x - sin x + tan x - 1=0 find value of x if x belongs to [0,2π]
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28x%29%2Atan%28x%29+-+sin%28x%29+%2B+tan%28x%29+-+1+=+0+
+sin%28x%29%2A%28+tan%28x%29+-+1+%29+%2B+%28+tan%28x%29+-+1+%29+=+0+
+%28+sin%28x%29+%2B+1+%29%2A%28+tan%28x%29+-+1+%29+=+0+
-------------------------------------
either:
(1) +sin%28x%29+=+-1+
or
(2) +tan%28x%29+=+1+
----------------------
For (1),
+x+=+3%2Api%2F2+
For (2)
+x+=+pi%2F4+
+x+=+5%2Api%2F4+
-----------------------
So, there are 3 answers in [ 0,2*pi]
-----------------------------------
check:
+sin%28x%29%2Atan%28x%29+-+sin%28x%29+%2B+tan%28x%29+-+1+=+0+
+x+=+3%2Api%2F2+

+%28-1%29%2A%281%2F0%29+-+%28-1%29+%2B+1%2F0+-+1+=+0+
I don't think this can be determined. Thar leaves 2 answers
+sin%28x%29%2Atan%28x%29+-+sin%28x%29+%2B+tan%28x%29+-+1+=+0+
+sin%28pi%2F4%29%2Atan%28pi%2F4%29+-+sin%28pi%2F4%29+%2B+tan%28pi%2F4%29+-+1+=+0+
+%28+sqrt%282%29%2F2+%29%2A1+-+sqrt%282%29%2F2+%2B+1+-+1+=+0+
+0+=+0+
and, also:
+sin%28x%29%2Atan%28x%29+-+sin%28x%29+%2B+tan%28x%29+-+1+=+0+

+%28-sqrt%282%29%2F2%29%2A1+-+%28-sqrt%282%29%2F2%29+%2B+1+-+1+=+0+
+0+=+0+
---------------
+x+=+pi%2F4+
+x+=+5%2Api%2F4+
are the answers
get another opinion, definitely


Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
+x+=+pi%2F4+
+x+=+5%2Api%2F4+
are the answers.

Agree and confirm.
---------------

The value x = 3pi%2F2 is not in the domain of the left side of the original equation.