Quandaries
and Queries 

!Hello! My name is Jesus and I´m a secondary student. I´m trying to verify a trigonometric identity but I don´t know how to do it.please help me!!!!!!!!!. The identity is : tan55º.tan65º.tan75º=tan85º (the sign (.) indicates multiplication) Thank you. 

Hi Jesus, This is not an identity, it is an equation. A trigonometric identity has variables in it and teh statement is true regardess of the values of the variables. This result is true but we don't see any nice way to see it. We would like to prove an identity that, for a specific value of the variable, gives your equation, but we don't see how. Anyway you can prove the expression is true using the fillowing identities.
Write
as
or, using the identities above again
Using cos140 = cos(180  40) = cos40, sin30 = cos60 and similar expressions, the equation to prove can be written as
which is
or, finally
Since cos60 = ^{1}/_{2}, the left side is
Using the second identity at the top of the page one last time, the right side is
Thus your equation is true. Chris and Penny 

