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# C2 - Trig identities

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1. C2 - Trig identities
I've looked at a few threads and my notes on trig identities, but this question continues to baffle me.

Question: Prove that, for all values of x, the value of the expression

is an integer and state its value.

I have expanded and simplified it to get . I know you are supposed to substitute the for , giving me .

But why can't you substitute for instead? Or both?

Even after that, I'm not sure what I am meant to do or how to determine the answer. The mark scheme says the answer is 10, but how do you get it?

2. Re: C2 - Trig identities
expand it

10-(10-sin^2x)+(10sin^2x)

EQUALS

10.

(Original post by Prestoria)
I've looked at a few threads and my notes on trig identities, but this question continues to baffle me.

Question: Prove that, for all values of x, the value of the expression

is an integer and state its value.

I have expanded and simplified it to get . I know you are supposed to substitute the for , giving me .

But why can't you substitute for instead? Or both?

Even after that, I'm not sure what I am meant to do or how to determine the answer. The mark scheme says the answer is 10, but how do you get it?

3. Re: C2 - Trig identities
(Original post by Prestoria)
I've looked at a few threads and my notes on trig identities, but this question continues to baffle me.

Question: Prove that, for all values of x, the value of the expression

is an integer and state its value.

I have expanded and simplified it to get . I know you are supposed to substitute the for , giving me .

But why can't you substitute for instead? Or both?

Even after that, I'm not sure what I am meant to do or how to determine the answer. The mark scheme says the answer is 10, but how do you get it?

We know that,

So
4. Re: C2 - Trig identities
(Original post by Prestoria)
I've looked at a few threads and my notes on trig identities, but this question continues to baffle me.

Question: Prove that, for all values of x, the value of the expression

is an integer and state its value.

I have expanded and simplified it to get . I know you are supposed to substitute the for , giving me .

But why can't you substitute for instead? Or both?

Even after that, I'm not sure what I am meant to do or how to determine the answer. The mark scheme says the answer is 10, but how do you get it?

You can do all the things you said. But if you did both; you would just get back where you started.

Doing it the way you did it; you had

But note you can also write
Last edited by Intriguing Alias; 22-04-2012 at 20:38.
5. Re: C2 - Trig identities
what is equal to?
6. Re: C2 - Trig identities
(Original post by Prestoria)
I've looked at a few threads and my notes on trig identities, but this question continues to baffle me.

Question: Prove that, for all values of x, the value of the expression

is an integer and state its value.

I have expanded and simplified it to get . I know you are supposed to substitute the for , giving me .

But why can't you substitute for instead? Or both?

Even after that, I'm not sure what I am meant to do or how to determine the answer. The mark scheme says the answer is 10, but how do you get it?

The identity,

=

is derived from:

=

So...

Hope this helps!
7. Re: C2 - Trig identities
Oh, that was a dumb moment. Thanks guys, I understand it now!

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Last updated: April 22, 2012
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