Question

Verify identity:

csc^2 beta - cos^2 beta - sin^2 beta = cot^2 beta

Answer 1

csc^2 beta - cos^2 beta - sin^2 beta
=csc^2 beta - [cos^2 beta + sin^2 beta]
got this step, i just factored out - *minus*

Answer 2

okay

Answer 3

now you know what cos^2 beta + sin^2 beta simplifies to ?

Answer 4

1

Answer 5

so csc^2 beta -1 = cot^2 beta

Answer 6

\[\csc^2\beta-\cos^2\beta-\sin^2\beta = \cot^2\beta\]
\[\csc^2\beta -(\cos^2\beta+\sin^2beta) = \cot^2\beta\]
\[\csc^2\beta-1=\cot^2\beta\]

Answer 7

and that's probably on your identity sheet, right?

Answer 8

yes, @Summersnow8 , correct :)

Answer 9

but i cant use the sheet

Answer 10

@hartnn then what

Answer 11

csc^2 beta -1 = cot^2 beta
means you have verified your given identity,
you proved left side = right side

Answer 12

\[\cot^2\beta = \frac{1}{\tan^2\beta} = \frac{1}{\frac{\sin^2\beta}{\cos^2\beta}} = \frac{\cos^2\beta}{\sin^2\beta}\] and
\[\csc^2\beta = \frac{1}{\sin^2\beta}\]so you have \[\frac{1}{\sin^2\beta}-1=\frac{\cos^2\beta}{\sin^2\beta}\]

\[\frac{1}{\sin^2\beta}-\frac{\sin^2\beta}{\sin^2\beta}=\frac{\cos^2\beta}{\sin^2\beta}\]
and using an identity you already used, you can see that is true...

Answer 13

(look at the numerators)

Answer 14

you still have doubts ?

Answer 15

yeah, but it is okay. I can't make sense of these problems, 7 hours...... im ready to just throw in the towel

Answer 16

1-sin^2 = cos^2 right? cos^2 + sin^2 = 1

Answer 17

but you have already verified it completely, let me list out the steps
\(left \:\:side =\csc^2\beta-\cos^2\beta-\sin^2\beta \\ =\csc^2\beta -(\cos^2\beta+\sin^2 \beta) =\csc^2 \beta-1 \\= \cot^2\beta = right \:\:side \)
hence verified

Answer 18

i cant think anymore.

Answer 19

I know the feeling :-)

Answer 20

thanks anyway

Answer 21

take a fresh look at it tomorrow.

Answer 22

it is due tomorrow, can't

Answer 23

okay, later tonight. take a 15 minute brisk walk. light exercise helps...

Answer 24

i rather just give up, this is stupid