Thread: How 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!

Originally Posted by azuresonata

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


Mr F says: At a glance, I'd suggest making the sustitutions and on each side and then simplifying the resulting expressions.



Mr F says: At a glance I'd suggest substituting from the double angle formulae in the left hand side and simplifying the resulting expression.



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

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) = ......

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!)