I was doing an advance reading on trigonometry (identities, specifically) when I encountered these problems on verification:

I'll try to edit this when I come up with answers. Thanks for those who will help!

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- September 11th 2008, 04:25 AMazuresonataHow do I verify these identities?
I was doing an advance reading on trigonometry (identities, specifically) when I encountered these problems on verification:

I'll try to edit this when I come up with answers. Thanks for those who will help! - September 11th 2008, 05:00 AMmr fantastic
For the last, you can start by using the following identities (derivable from the compound angle formulae):

1. sin(A + B) + sin(A - B) = 2 sin A cos B.

From which it follows that:

sin(x) + sin(3x) = 2 sin(2x) cos(x)

sin(5x) + sin(7x) = 2 sin(6x) cos(x)

2. cos(A + B) + cos(A - B) = 2 cos A cos B.

From which it follows that

cos(x) + cos(3x) = ........

cos(5x) + cos(7x) = ...... - September 11th 2008, 05:03 AMthelostchild
ok for problems such like this knowing the standard identities is VERY useful, a list of them can be found here

Table of Trigonometric Identities

for example lets look at the first of your problems

looking at the denominator we can write it as

so the LHS becomes

now writing tan x in terms of sine and cosine we have

then using

once again writing tan in terms of sine and cosine gives us the RHS

so all this topic is really is learning identities and practice (hence why this is deathly boring!)