Answer:
x = 2k[tex]\pi[/tex] is the solution of this equation.
Step-by-step explanation:
This question is related to trigonometric equations.
The given equation is,
[tex]sin^{2} x + 3cos x - 1 = 2[/tex]
We have to find the solutions of this equation.
Put [tex]sin^{2}x = 1 - cos^{2}x[/tex]
[tex]1 - cos^{2}x[/tex] + 3cosx - 1 = 2
[tex]cos^{2}x -3cosx+2[/tex] = 0
For this equation only cosx = 1 is possible solution.
Cosx = 1 happens when x is a multiple of 2[tex]\pi[/tex]
So x = 2k[tex]\pi[/tex] is the solution of this equation.
