Question

Simplify the trigonometric expression.

Answer 1

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

Answer 2

multiply numerator and denominator by 1+ cos theta

Answer 3

then you can use the relation,
\((a+b)(a-b)=a^2-b^2\)

Answer 4

That doesn't seem right

Answer 5

what doesn't seem right ?
"multiplying numerator and denominator by 1+ cos theta" ?
have you tried it ?

Answer 6

yes, i tried it.. the answer doesnt seem right

Answer 7

there's an another way too, if this feels confusing...
what answer u got ?

Answer 8

i got sin theta

Answer 9

naah...how ?
the denominator :
(1+ cos theta )(1- cos theta) = 1-cos^2 theta =...... ?

Answer 10

I'm not good at math, none of this is making sense to me...

Answer 11

none!? my heart just broke :P
\(\large \frac{ \sin^2 \theta }{ 1- \cos \theta }=\frac{( \sin^2 \theta )(1+cos \theta)}{( 1- \cos \theta)(1+cos \theta) }=\frac{( \sin^2 \theta )(1+cos \theta)}{1-\cos^2 \theta }\)
using \((a+b)(a-b)=a^2-b^2\)

Answer 12

got that^ ?

Answer 13

OKay yeah that makes some sense

Answer 14

and what does 1- cos^2 theta equal to ??
(hint : \(\sin^2 x+\cos^2x=1\))

Answer 15

Does'nt it = sin^2 theta?

Answer 16

or am i totally just getting this wrong?

Answer 17

it exactly = sin^2 theta!
good :)
so, what gets cancelled ? what remains ?

Answer 18

the sin^2 theta's get cancelled?

Answer 19

wait not the cos gets cancelled

Answer 20

the sin^2 theta's get cancelled,
what remains is 1+cos theta
thats your answer.

Answer 21

thanks :)

Answer 22

welcome ^_^