Using identities (sum and difference examples)

Here are my two examples, i wasnt sure of what i was doing, but
βεθany was nice enough to help me out!!


Example 1:

Simplify: sin6x sin4x - cos6x cos4x

(for this you will have to use the identity) :
cos(α+β)= cosαcosβ - sinαsinβ

sin6x sin4x - cos6x cos4x =
-(cos6xcos4x - sin6xsin4x) = -cos(6x+4x) =
-cos10x

Example 2:
Determine the exact value of sin 75°

To begin, use the identity: sin(α+β) = sinαcosβ

sin(30+45) =sin 30cos 45 + cos 30 sin 45

= 1/2(√2/2) + √3/2(√2/2)

=√2/4 + √6/4

=√6+√2 /4