Evaluate the angles using sums as products or products as sums. (1) sin (75 degrees -15 degrees) 2) cos (65 degrees - 25 degrees)

Question

Using either the sums as products or products as sums to work out the answer.

Answer 1

Greetings! Lets solve this shall we ?

We must use the trig identities to solve these expressions such that

sin(α-β) = sinαcosβ - cosαsinβ

and

cos(α-β) = cosαcosβ + sinαsinβ

Then,

sin(75-15) = sin75cos15 - cos75sin15

and

cos(65-25) = cos65cos25 + sin65sin25

I hope this helped!