sec^2x=1-tanx

Question

sec^2x=1-tanx

0≤x≤2π

Answer 1

sec²x = 1 - tanx            identity

1 + tan²x = 1 - tanx      subtract 1 from both sides

tan²x = - tanx               add tanx to both sides

tan²x + tanx = 0           factor

tanx (1 + tanx) = 0       zero product rule

 

tanx = 0

tan^-1 0 = x

x ∈ {0. π}

 

1 + tanx = 0

tanx = -1

tan^-1 x = -1

x ∈ {3π/4, 7π/4}