# How to use the product-to-sum formula to write the product as a sum or difference? 4 cos pi/3 sin 5pi/6

##
Need Help

Need Help

By signing up, you agree to our Terms of Service and Privacy Policy

To use the product-to-sum formula to write the product ( 4 \cos(\frac{\pi}{3}) \sin(\frac{5\pi}{6}) ) as a sum or difference, you can apply the formula:

[ \sin(A) \cos(B) = \frac{1}{2} [\sin(A + B) + \sin(A - B)] ]

In this case, ( A = \frac{\pi}{3} ) and ( B = \frac{5\pi}{6} ). Plug these values into the formula:

[ \sin\left(\frac{\pi}{3}\right) \cos\left(\frac{5\pi}{6}\right) = \frac{1}{2} \left[\sin\left(\frac{\pi}{3} + \frac{5\pi}{6}\right) + \sin\left(\frac{\pi}{3} - \frac{5\pi}{6}\right)\right] ]

Now, simplify the expressions inside the sine functions:

[ \sin\left(\frac{\pi}{3} + \frac{5\pi}{6}\right) = \sin\left(\frac{\pi}{2}\right) = 1 ] [ \sin\left(\frac{\pi}{3} - \frac{5\pi}{6}\right) = \sin\left(-\frac{\pi}{2}\right) = -1 ]

Substitute these values back into the formula:

[ \frac{1}{2} [1 - (-1)] = \frac{1}{2} \times 2 = 1 ]

Therefore, ( 4 \cos\left(\frac{\pi}{3}\right) \sin\left(\frac{5\pi}{6}\right) ) can be written as ( 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7