Question

Verify.

Answer 1

verify what

Answer 2

\[\frac{ \cos \theta }{ 1-\sin \theta }=\frac{ \sin \theta-\csc \theta }{ \cos \theta-\cot \theta }\]

Answer 3

Go from the right hand side
numerator: sin -1/sin = (sin^2 -1)/ sin = -cos^2/sin

Answer 4

denominator: cos - cos/sin= (sincos -cos)/sin

Answer 5

combine the two, we don't have sin at the denominator of both them, right? now it is
\(\dfrac{-cos^2\theta}{sin\theta cos\theta -cos\theta}\)

Answer 6

\(\dfrac{cos\theta}{1-sin\theta}\)

Answer 7

dat sit

Answer 8

How did the cos in the numerator become positive?

Answer 9

switch the term from denominator to get -1 out, cancel out with numerator

Answer 10

sin cos - cos = -(cos -sin cos)

Answer 11

in other word, factor -cos out

Answer 12

get it?

Answer 13

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

Answer 14

ok?

Answer 15

Yes, but 1-sin is not sin-1. They're not the same.

Answer 16

hey, your left hand side is cos / 1 - sin and I got it, right?

Answer 17

Oh my god. Yes it is.

Answer 18

ok

Answer 19

Thank you

Answer 20

yw