Question

Verify the identity. sin(3pi - x) = sinx

Answer 1

Remember that Sin(x+y) = Sin(x)Cos(y) - Sin(y)Cos(x)

Knowing that, can't we just call the whole thing:

Sin(3pi + (-x))

From there, we apply the identity

Sin(3pi)Cos(x) - Sin(x)Cos(3pi)

We know that Sin(3pi) = 0, and Cos(3pi) = -1

Sin(3pi)Cos(x) - Sin(x)Cos(3pi)

= (0) Cos(x) - Sin(x) (-1)

Anything times zero is zero, and two negatives make a positive so:

= 0 + Sin(x)

= Sin(x)

Answer 2

oh hang on it should be -x and it should be Sin(3pi)Cos(x) + Sin(x)Cos(3pi)

Answer 3

yeah i understand. all i was confused about was how to simplify further after using the sum and difference formula things. Thanks!