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

Question

(1+sin²x)/(cos²x)=1+2tan²x

Answer 1

(1+sin^2)/cos^2= 1 +2(sin^2)/cos2 [find common denominator onthe left side and change tan^2 to sin^2/cos^2]

1/cos^2 +sin^2/cos^2= 1+ 2sin^2/cos^2 [subtract sin^2/cos^2 from both sides]

1/cos^2= 1+sin^2/cos^2[subtract 1 from both sides]

1/cos^2 -1 = sin^2/cos^2[ find common denominator on left side]

1/cos^ 2- cos^2/cos^2 = sin^2/cos^2[combine fractions on left side]

1-cos^2/cos^2 = sin^2/cos^2 [ use the identity 1-cos^2 = sin^2

sin^2/cos^ = sin^2/cos^2