Question

Find cos(x) if
`(sin^2x-1)/(cosx) =-1`.
A -1
B 2
C 1
D 0

Answer 1

(sin²(x) - 1)/cos(x) = -1

-cos²(x)/cos(x) = -1

-cos²(x) = -cos(x)

cos²(x) - cos(x) = 0

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

Then it follows that cos(x) = 0 or cos(x) = 1. But if cos(x) = 0, then the original expression on the left side of the equation would be undefined. Then C is the only valid solution.