Answer:
x = 90, 199.5, 270, 340.5 degrees
Step-by-step explanation:
cos2x + 2sinx = sin^2x
Change cos2x to 1 - 2sin^2x:
1 - 2sin^2x + 2 sinx = sin^2x
Shift the terms to make it a quadratic equation:
3 sin^2x - 2sinx - 1 = 0
Factorise the quadratic equation:
(sinx - 1)(3sinx + 1) = 0
sin x = 1 or sin x = -1/3
Solve for sin x = 1:
From graph of sin x, x = 90 and 270 degrees when sin x = 1.
x = 90, 270 degrees
Solve for sin x = -1/3
Sin x = -1/3
Basic angle = sin inverse (1/3)
= 19.471 degrees
Since sin x < 0, x is in the 3rd or 4th quadrant
x = 180 + 19.471, 360 - 19.471
x = 199.5, 340.5
Hence, x = 90, 199.5, 270, 340.5 degrees
[Sorry if I am wrong :( ]
