1975 AHSME Problems/Problem 30
Problem 30
Let . Then
equals
Solution
Using the difference to product identity, we find that
is equivalent to
Since sine is an odd function, we find that
, and thus
. Using the property
, we find
We multiply the entire expression by
and use the double angle identity of sine twice to find
Using the property
, we find
Substituting this back into the equation, we have
Dividing both sides by
, we have