Question

Which expression is equivalent to sin(1) cos(15) - cos(7) sin(79)?"

a). cos(2)cos(2)
b). cos(3)cos(3)
c). sin(2)sin(2)
d). sin(3)sin(3)

Answer 1

The expression sin(1)cos(15) - cos(7)sin(79) simplifies to sin(16)cos(14) + sin(72)cos(72).

Step-by-step explanation:

The expression sin(1)cos(15) - cos(7)sin(79) can be simplified using the product-to-sum identities and trigonometric identities. Using the product-to-sum identity sin(a)cos(b) = (1/2)[sin(a+b) + sin(a-b)], the expression can be written as (1/2)[sin(1+15) + sin(1-15)] - (1/2)[sin(7+79) + sin(7-79)].

Next, using the sum-to-product identity sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2), the expression can be further simplified to (1/2)[2sin(16)cos(14) - 2sin(-72)cos(72)].

Finally, simplifying the expression gives sin(16)cos(14) + sin(72)cos(72).