tan²x + sec²x =1
tan = sin /cos
sec = 1/cos
sin^2 x/cos^2 x + 1/ cos ^2 x = 1
since it has a common denominator
(sin ^2 x+1 ) /cos ^2 x = 1
multiply by cos ^2 x on each side
sin ^2 x + 1 = cos ^2 x
replace 1 = sin^2 + cos ^2
sin ^2 x + sin ^2 x + cos^2 x = cos ^2 x
combine like terms
2 sin ^2 x + cos ^2 = cos ^ 2 x
subtract cos ^2 x from each side
2 sin^2 x = 0
divide by 2 on each side
sin^2 x =0
take the square root on each side
sin x = 0
take the arcsin on each side
arcsin (sin x) = arcsin (0)
x = 0,pi, 2* ip
x = n* pi where n is an integer