sec^(2)x+tanx=1find all solutions of the equation in the interval [0,2\pi )

Answer 1

secx = 1/cosx

tanx = sinx/cosx

1/cos^2x + sin^2x/cos^x = 1

(1+sin^2x)/cos^2 = 1

1+ sin^2x = cos^2x

1 = cos^2x + sin^2x

cos^2x + sin^2x + sin^2x = cos^2x

2sin^2x = 0

sin^2x = 0

sinx = 0

x = pi

if you don't know what to do, it's often helpful to convert everything into sines and cosines

check the answer

sec^2(pi) + tan(pi) = 1

(-1)^2 + 0 = 1