Prove the identity

Thanks in advance

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- Dec 26th 2009, 05:48 AMPunchHelp required on solving Trigo sum..
Prove the identity

Thanks in advance - Dec 26th 2009, 05:54 AMe^(i*pi)
- Dec 26th 2009, 06:11 AMPunch
- Dec 26th 2009, 06:21 AMPunch
so since

For , starting with LHS,

how do i continue? - Dec 26th 2009, 07:02 AMskeeter
- Dec 26th 2009, 07:07 AMe^(i*pi)
Yeah, I was working on the left side to get the right. Just found it easier to simplify the numerator first.

Yeah (you can derive this from )

Quote:

For , starting with LHS,

how do i continue?

Then you'll want to make this into one fraction and since the LCM is we'll use that.

As these have the same denominator we can combine fractions so the above is equal to

You should know that from your double angle identities that and you should also know that when dividing by a fraction we flip it and multiply.

From the definition of sec: so that cancels to leave and again from the definition of sec:

Since this is equal to the RHS we've proved the identity is true