is the value 3pi/2 is a solution for the equation 2sin^2x-sinx-1=0
False
To determine if the value 3π/2 is a solution for the equation 2sin^2(x) - sin(x) - 1 = 0, we need to substitute this value into the equation and check if it satisfies the equation.
Step 1: Start with the equation 2sin^2(x) - sin(x) - 1 = 0.
Step 2: Substitute x with the given value 3π/2.
2sin^2(3π/2) - sin(3π/2) - 1 = 0
Step 3: Simplify the equation using trigonometric identities:
sin(3π/2) = -1 (since the sine of π/2 is 1 and sine is periodic with a period of 2π)
2sin^2(3π/2) - sin(3π/2) - 1 = 2(-1)^2 - (-1) - 1 = 2 - (-1) - 1 = 2 + 1 - 1 = 2 + 0 = 2
Step 4: Determine if the equation is satisfied.
The equation becomes:
2 = 0
Since 2 does not equal 0, the value 3π/2 is not a solution for the equation 2sin^2(x) - sin(x) - 1 = 0.
sin 3 pi/2 = -1
2(-1)^2 -(-1) -1
2 + 1 - 1
2
Looks like a typo to me. Perhaps it should be
2 sin^2x + sinx - 1 = 0