trig help please?

Question

If (1 + tan^2 x)\(sec x) = sin^2 x + (1)\(sec^2 x) find the value of cos x

Answer 1

1 + tan^2 x = sec^2 x
1 / sec^2 x = cos^2 x

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

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

sec x = 1 same as 1 / cos x = 1 or cos x=1

Answer 2

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

(1 + tan^2x) / secx = cosx (1 + tan^2x)

cosx + sin^2x/cosx = 1

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

1 = cos x