Use a compound angle formula for sine to show that

sine2(theta) = 2sine(theta)cos(theta)

Take this formula

Sin(A+B)= SinAcosB+ SinBcosA
now make A=b and you have it.

if the tangent of 44 degrees is .966 what is the cotangent of 46 degrees

To prove the compound angle formula for sine, we need to express both sides of the equation using the definitions and properties of sine and cosine functions. Here's how we can do it:

Starting with the left side of the equation: sine^2(theta)
We can rewrite this as (sine(theta))^2 using the exponent rule.

Now let's focus on the right side of the equation: 2sine(theta)cos(theta)
We know that the double angle formula for sine is sin(2theta) = 2sin(theta)cos(theta).

So, we can rewrite the right side of the equation as sin(2theta). However, we want to prove sine^2(theta) = sin(2theta) instead.

To convert sin(2theta) to sine^2(theta), we can use the double angle formula for sine, which states that sin(2theta) = 2sin(theta)cos(theta).

Now we can substitute sin(2theta) in the equation with 2sin(theta)cos(theta):

sine^2(theta) = 2sin(theta)cos(theta)

And that proves the compound angle formula for sine: sine^2(theta) = 2sin(theta)cos(theta).

In summary, we started by expressing the left side of the equation and then used the double angle formula for sine to manipulate the right side of the equation, eventually showing that the two sides are equal.