# Thread: solve this trigonometric equation: [(2sinx+1)/(cosx)]*(cosx-sinx)+2=0

1. ## solve this trigonometric equation: [(2sinx+1)/(cosx)]*(cosx-sinx)+2=0

Solve this trigonometric equation:

[(2sinx+1)/(cosx)]*(cosx-sinx)+2=0

2. Originally Posted by spartas
[(2sinx+1)/(cosx)]*(cosx-sinx)+2=0
What did you mean by "solve this trigonometric equation"?

Are you trying to calculate the value of "x", from the given equation?

3. to find the x, it has to do with tangent half-angle formulas!

4. Originally Posted by spartas
to find the x, it has to do with tangent half-angle formulas!
Okay - What is that formula? What does it looklike?

5. i have to replace the sinx with sinx=2t/1+t^2 cosx=1-t^2/1+t^2
now it looks like
$\frac{2\frac{2t}{1+t^{2}}+1}{\frac{1-t^{2}}{1+t^{2}}}\times(\frac{1-t^{2}}{1+t^{2}}-\frac{2t}{1+t^{2}})+2=0$

6. Originally Posted by spartas
i have to replace the sinx with sinx=2t/1+t^2 cosx=1-t^2/1+t^2
In future, kindly please include all of the instructions when you post the exercise. Thank you!

Originally Posted by spartas
now it looks like
$\frac{2\frac{2t}{1+t^{2}}+1}{\frac{1-t^{2}}{1+t^{2}}}\times(\frac{1-t^{2}}{1+t^{2}}-\frac{2t}{1+t^{2}})+2=0$
Okay, so you're left with just algebra to do. Use what you learned about complex fractions (here), solving polynomials (here), and the Quadratic Formula (here) to simplify and solve.

. . .the equation you posted:

. . . . .$\dfrac{\left(2\frac{2t}{1\, +\,t^{2}}\,+\,1\right)}{\left(\frac{1\,-\,t^{2}}{1\,+\,t^{2}}\right)}\, \times\, \left(\dfrac{1\,-\,t^{2}}{1\,+\,t^{2}}\,-\,\dfrac{2t}{1\,+\,t^{2}}\right)\,+\,2\,=\,0$

. . .combining w/ common denominators:

. . . . .$\dfrac{\left(\frac{4t\, +\, (1\, +\, t^2)}{1\, +\, t^2}\right)}{\left(\frac{1\, -\, t^2}{1\, +\, t^2}\right)}\, \times\, \left(\dfrac{1\, -\, t^2\, -\, 2t}{1\, +\, t^2}\right)\, +\, 2\, =\, 0$

. . .doing some simplification:

. . . . .$\left(\dfrac{4t\, +\, 1\, +\, t^2}{1\, -\, t^2}\right)\, \times\, \left(\dfrac{1\, -\, 2t\, -\, t^2}{1\, +\, t^2}\right)\, +\, 2\, =\, 0$

Multiply through by the denominators to clear the fractions, and so forth. If you get stuck in finding the four solutions, please reply showing all of your steps so far, starting with the ones displayed above. Thank you!