Sine minus sine is cos?

[autumnfaerie]

I was given the problem:

Subtract:
1/sin theta minus sin theta


Ok, I treated it like any other subtraction of two unlike fractions and multiplied both sides by "sin theta" to get a common denomenator and was wrong. The back of the book gives the answer

cos[sup:39r53g9o]2[/sup:39r53g9o] theta
sin theta

How in the world did they get that? I know I have to be missing something obvious...

TIA!

 

[mmm4444bot]

You need to write sin(theta)/1 as an equivalent fraction such that it has a denominator of sin(theta), so that you can then subtract it from 1/sin(theta).

Multiply sin(theta)/1 by sin(theta)/sin(theta).

You'll then have a common denominator.

SYMBOLIC EG:

1/A - A

1/A - A * (A/A)

1/A - A^2/A

(1 - A^2)/A

 

[autumnfaerie]

Ok, I see what I did wrong now. That and not having the Pythagorean Identities completely memorized yet. Thanks!

 

[Deleted member 4993]

I was given the problem:

Subtract:
1/sin theta minus sin theta


Ok, I treated it like any other subtraction of two unlike fractions and multiplied both sides by "sin theta" to get a common denomenator and was wrong. The back of the book gives the answer

cos[sup:25xis95x]2[/sup:25xis95x] theta
sin theta

How in the world did they get that? I know I have to be missing something obvious...

TIA!

How in the world did they get that?
because

\(\displaystyle \sin^2(\theta) \, + \, \cos^2(\theta) \, = \, 1\)

another one to remember

\(\displaystyle \sec^2(\theta) \, = \, 1 \, + \, \tan^2(\theta)\)

 

[mmm4444bot]

I'm thinking that the original poster used underlining to "draw" a fraction bar, but superscript code elevates the underlining below the exponent. (I thought I saw a subtraction, when I first looked at it.)

In other words, I'm thinking that they intended to post cos(theta)^2/sin(theta).

 

[Denis]

Re:

In other words, I'm thinking that they intended to post cos(theta)^2/sin(theta).

You're not paid to think :evil:

 

[mmm4444bot]

You're not paid to think :evil:

Tell me.

Outrageous, isn't it?

When I get my hands on whoever's had the responsibility over the last 20 years, it damn-well better be retroactive.

(Oops -- that wasn't quite humble. Darn it. Now look what you made me do, Denis.)