Solve the equation for principal values of x. Express solutions in degrees.

sinx = 1 + cos^2x

a. 45°
b.180°
c. 90°
d. 270°

Option C:

x = 90°

Solution:

Given equation:

To find the degree:

Subtract 1 + cos²x from both sides.

Using the trigonometric identity:

Let sin x = u

Factor the quadratic equation.

u + 2 = 0,  u – 1 = 0

u = –2, u = 1

That is sin x = –2, sin x = 1

sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.

sin x = 1

The value of sin is 1 for 90°.

x = 90°.

Option C is the correct answer.

the most boring thing ever written

step-by-step explanation:

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