Question

Simplify the trigonometric expression

Answer 1

\[1/1+Sin \theta+ 1/1-\]

Answer 2

do you mean
\(\dfrac{1}{1+\sin \theta}+\dfrac{1}{1-\sin \theta}\)
??

Answer 3

yes like that, sorry

Answer 4

do you know how to multiply and divide by conjugate expression ?

Answer 5

i'm afraid not

Answer 6

\(\dfrac{1}{1+\sin \theta} \times \dfrac{1-\sin \theta}{1-\sin \theta}+\dfrac{1}{1-\sin \theta}\times \dfrac{1+\sin \theta}{1+\sin \theta}\)
i did that ^ to make the common denominator as (1+sin )(1- sin)
could you notice and understand that ?

Answer 7

yes i understand what you did but i'm a little confused as to how i would solve that?

Answer 8

first see the denominator
\((1+\sin \theta)(1-\sin \theta)=... ?\)

Answer 9

\[\sin \theta\] is the denominator?

Answer 10

i don't understand what made you ask that question...

Answer 11

\((a+b)(a-b)=a^2-b^2 \\ (1+\sin \theta)(1-\sin \theta)=... ? \)

Answer 12

1\[1^{2}-\sin \theta ^{2}\] ?

Answer 13

i didnt mean to put that "1" at the top.

Answer 14

and what is \(1- \sin^2 \theta =... ?\)
use \(\sin^2 \theta +\cos^2 \theta =1\)

Answer 15

\[\cos ^{2} \theta ? \]

Answer 16

yes.
so you now have
\(\dfrac{1-\sin \theta}{\cos^2 \theta}+\dfrac{1+ \sin \theta}{\cos^2 \theta}\)
you know what can u do in next step ??

Answer 17

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

Answer 18

when denominators are same you can combine the numerator...