Question

Prove the following Identity

1/cos(theta) - cos(theta)/1+sin(theta)=tan(theta)

Answer 1

\[\frac{ 1 }{ \cos \theta } - \frac{ \cos \theta }{ 1+\sin \theta } = \frac{ 1+\sin \theta-\cos ^{2} \theta }{ \cos \theta(1+\sin \theta ) }\]

Answer 2

\[-\cos ^{2} \theta = -1+\sin ^{2} \theta \]

Answer 3

\[\frac{ \sin ^{2} \theta + \sin \theta}{ \cos \theta (1+\sin \theta) } = \frac{ \sin \theta (1+\sin \theta) }{ \cos \theta (1+\sin \theta) }= \frac{ \sin \theta }{ \cos \theta} = \tan\]

Answer 4

Firstly, thanks for the response. I have a question, where did you get -cos^2(theta) in the first step in numerator?

Answer 5

dont know how to explain it but this is what u do when u add two fractions

Answer 6

thank you, I understand it better now friend

Answer 7

great
good luck