Question

Verify the identity. sin(x) tan (x/2) = 1 − cos(x)

Answer 1

To verify the given identity sin(x) tan(x/2) = 1 − cos(x), we can simplify both sides using trigonometric identities and show that they are equal.

Step-by-step explanation:

We can verify the given identity using trigonometric identities and simplifying both sides of the equation.

Starting with the left side:

• sin(x) tan(x/2) = sin(x) * (sin(x/2) / cos(x/2)) = (sin(x) * sin(x/2)) / cos(x/2)

Now, simplifying the right side:

• 1 - cos(x) = (1 - cos(x))*(1 + cos(x)) / (1 + cos(x)) = (1 - cos^2(x)) / (1 + cos(x)) = sin^2(x) / (1 + cos(x))

Since both sides simplify to the same expression, the given identity is verified.