Question

Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.cos(cos ( 16 ) - sin ()sin ( 15 )-Зл10

Answer 1

Hello!

We have the expression below:

$\cos (\frac{\pi}{2})\cos (\frac{3\pi}{10})-\sin (\frac{\pi}{2})\sin (\frac{3\pi}{10})$

Let's remember how we can use the sum identity formula:

$\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)$

Knowing it, let's use this property:

$\cos (\frac{\pi}{2})\cos (\frac{3\pi}{10})-\sin (\frac{\pi}{2})\sin (\frac{3\pi}{10})=\cos (\frac{\pi}{2}+\frac{3\pi}{10})$

Let's solve the sum:

$\cos (\frac{\pi}{2}+\frac{3\pi}{10})=\cos (\frac{5\pi+3\pi}{10})=\cos (\frac{8\pi}{10})$

We can simplify it by two:

$\cos (\frac{8\pi}{10})=\cos (\frac{4\pi}{5})$

Answer:

cos(4pi/5)