Find all solutions of the equation in the interval[0, 2π) tan^2x−secx=−1

Answer 1

tan^2x = sec^2x -1

sec^2x-1 - secx = -1

sec^2x - secx = 0

secx(secx- 1) = 0

secx =0 and secx =1,

1/cosx = 1

cosx = 1

x = 0 is the only solution

the parentheses instead of bracket for 2pi means 2pi isn't in the interval.

secx=0 means

1/cosx = 0, and cosx = infinity, but cosine is always less than or equal to one

secx>1 or less than -1, never = 0

Answer 2

SIn^2-cos=-cos^2

Sin^2+cos^2-cos=0

1-cos=0

1=cos

X=0