Question

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.

a) 2sin(x)cos(x)
b) sin(x)
c) cos(x)
d) tan(x)

Answer 1

To simplify the expressions, we can use the Double-Angle Formula for sin(2x) in part a) and the Half-Angle Formula for tan(x/2) in part d). Parts b) and c) do not require simplification.

Step-by-step explanation:

To simplify the expression using a Double-Angle Formula or a Half-Angle Formula, let's consider each part:

1. a) 2sin(x)cos(x): We can use the Double-Angle Formula for sin(2x) to simplify this expression. sin(2x) = 2sin(x)cos(x), so the expression simplifies to sin(2x).
2. b) sin(x): There is no need to simplify this expression.
3. c) cos(x): There is no need to simplify this expression.
4. d) tan(x): We can use the Half-Angle Formula for tan(x/2) to simplify this expression. tan(x/2)
5. = sin(x)/(1+cos(x)).