Question

100 POINTS!!! can someone please explain how to do this?

Find all exact solutions on the interval [0, 2π). Look for opportunities to use trigonometric identities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
sin²(x) - cos²(x) - sin²(x) = 0
x =

Answer 1

x = π/2, 3π/2

Explanation:

sin²(x) - cos²(x) - sin²(x) = 0

-cos²(x) = 0

cos²(x) = 0

cos(x) = 0

x = π/2, 3π/2

Answer 2

x =pi/2,3pi/2

Explanation:

sin²(x) - cos²(x) - sin²(x) = 0

Simplify

sin²(x) - sin²(x) = 0

Leaving us with

- cos²(x) = 0

Divide each side by -1

- cos²(x/-1 = 0/-1

cos²(x) = 0

Take the square root of each side

sqrt( cos²(x)) = sqrt(0)

cos(x) = 0

Taking the inverse cos of each side

cos^-1(cos(x)) = cos^-1(0)

x = pi/2 x = 3pi/2