please help me to solve this two questions, thanks!

lqq889 · 2012-07-14 16:55:22

1. prove that

hence, find all the angles between 0 and pi for which

2. The expresson

, make X the subjust and hence integrate with respect to y.

thanks

Last edited by lqq889 (2012-07-14 16:56:06)

Bob · 2012-07-14 19:33:33

hi lqq889

Q1. There's a formula that will help here.

This changes a sum of cosines into a product of cosines.

So how do you use it?

Take the first two terms that are added.

Put A = P+Q and 2A = P-Q and work out P and Q.

Do a similar substitution with 3A = P+Q and 4A = P-Q.

That way the LHS reduces to the sum of two terms.

It factorises and you can use the formula once more to reduce the remaining sum to two more factors. That should be the RHS.

Q2.

so

Bob

lqq889 · 2012-07-15 14:22:38

thanks bob for your help. btw how to find all the angles between 0 and pi for which

Last edited by lqq889 (2012-07-15 14:23:31)

Bob · 2012-07-15 19:22:37

hi lqq889

If 4 terms add up to zero, you cannot say much about them.

But if they multiply to make zero, then one or more of them must be zero.

So put the RHS of the identity equal to zero and consider that each factor might be zero.

Obviously '4' isn't but any of the cosines might, so solve cosA = 0, cosA/2 = 0 and cos5A/2 = 0.

Pick the values of A that are in range. (NOTE: it is A that must be in range, not eg. 5A/2)

Bob

lqq889 · 2012-07-20 16:49:31

Thanks bob for helping, I am understood, thanks very much.

Bob · 2012-07-20 20:40:07

You're welcome!

Bob

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