Question

How can I do this trigonometric identity question?

Answer 1

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

Answer 2

okay there, any attempt?

Answer 3

where did you stuck

Answer 4

Okay. So I figured to expand the term first. \[\sec^2 \theta + 2 \sec \theta \tan \theta + \tan^2 \theta\]

Answer 5

I don't know what to do after this.

Answer 6

I suggest you to rewrite right side in terms of sin and cos.

Answer 7

hmm that is valid attempt, where is the difficulty

Answer 8

sec^2=1+tan^2
can be good here

Answer 9

Okay so \[\frac{ 1 }{ \cos^2\theta} + \frac{ 2 \sin \theta }{ \cos^2 \theta } + \frac{ \sin^2 \theta }{ \cos^2 \theta }\]

Answer 10

then write eveything in terms of sins and cos

Answer 11

before that use the identity i gave you

Answer 12

well you can do it that way too

Answer 13

now you have a common denominator

Answer 14

I mean rewrite right side from very beginning, but that could work too.

Answer 15

\[\frac{ (1+ \sin \theta)(1 + \sin \theta }{ (1 - \sin \theta)(1 + \sin \theta)}\]

Answer 16

gotta go, but you had the idea

Answer 17

\[\frac{ 1+\sin \theta }{ 1 - \sin \theta}\]

Answer 18

\[\blacksquare\]

Answer 19

Thanks for the help guys. :D

Answer 20

:)