Question

50 points please give step by step instruction

Answer 1

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 :( ]