SOLUTION: 2tan(x)sin(x)+2sin(x)=tan(x)+1. x is has to be from 0 to 360 inclusive. Solve for all values of x

Question 1206963: 2tan(x)sin(x)+2sin(x)=tan(x)+1. x is has to be from 0 to 360 inclusive.
Solve for all values of x
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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2tan(x)sin(x)+2sin(x)=tan(x)+1. x is has to be from 0 to 360 inclusive.

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    2tan(x)sin(x)+2sin(x)=tan(x)+1.


Collect everything in the left side

    2tan(x)sin(x) - tan(x) + 2sin(x) - 1 = 0.


Group the terms

    (2tan(x)sin(x) - tan(x)) + (2sin(x) - 1) = 0.


Factor

    tan(x)*(2sin(x)-1) + (2sin(x)-1) = 0,

    (tan(x)+1)*(2sin(x)-1) = 0.


Consider two cases.


    Case 1.  tan(x) +1 = 0  --->  tan(x) = -1  --->  x = 135°  or x = 315°.

    Case 2.  2sin(x)-1 = 0  --->  sin(x) = 1/2 --->  x =  30°  or x = 150°.


ANSWER.  The solutions are 30°, 135°, 150°, 315°.

Solved.

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