Question

verify: 1- sin^2theta/1-costheta = -costheta

Answer 1

sin^2theta+cos^2theta=1
1-sin^2theta=cos^2theta
so cos^2theta/1-costheta=cos^2theta-costheta

Answer 2

=costheta(costheta-1)

Answer 3

so would your first step be to find the common denominator?

Answer 4

1 - sin^2theta
-----------
1- costheta

= 1 - (1- cos^2theta)
-------------
(1-cos theta)

= 1 - (1+cos theta)(1-cos theta)
-----------------------
( 1-cos theta)

= 1 - ( 1 + COS THETA)

Answer 5

my answer should be negative though, right?

Answer 6

Last step is,

= 1 - 1 -cos theta
= -cos theta

Answer 7

but don't you cross out both the 1-costheta 's so you'd be left with 1+costheta

Answer 8

A clan is correct I though the problem was \[ \frac{ 1-\sin ^{2}\theta }{ 1-\cos}\]

Answer 9

oh... i don't understand the last step though

Answer 10

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

\( 1 - \sin^2 \theta = (1 - \cos \theta)(-\cos \theta) \)

\( 1 - \sin^2 \theta = -\cos \theta + \cos^2 \theta \)

\( \cos^2 \theta = -\cos \theta + \cos^2 \theta \)

\(0 = -\cos \theta\)

This is not an identity.

Answer 11

the 1 is separate

Answer 12

i should've made that more clear

Answer 13

You mean 1 is not in the fraction in the numerator, but it is in the denominator.

Answer 14

its neither

Answer 15

1/1 - sin^2theta/1-costheta = -costheta

Answer 16

^ hopefully that makes more sense

Answer 17

I still don't underestand it. You can use the equation editor or the draw tool to make it clear.