The following equation involves a trigonometric equation in

The following equation involves a trigonometric equation in quadratic form. Solve the equation on the interval I0,2x) 4 sin x 10 sin X-6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Type an exact answer in terms of R. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed O B. There is no solution.

Solution

4sin^2x = -10sinx - 6

4sin^2x + 10sinx +6 =0

4sin^2x + 6x +4x + 6 =0

2sinx(2sinx +3) +2(2sinx +3) =0

(2sinx+2)( 2sinx + 3) =0

sinx = -1 ;x = 3pi/2

sinx= -3/2 ( Not a solution)

x = 3pi/2