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 ((\pi)/(2))\cos ((3\pi)/(10))-\sin ((\pi)/(2))\sin ((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 ((\pi)/(2))\cos ((3\pi)/(10))-\sin ((\pi)/(2))\sin ((3\pi)/(10))=\cos ((\pi)/(2)+(3\pi)/(10))`

Let's solve the sum:

`\cos ((\pi)/(2)+(3\pi)/(10))=\cos ((5\pi+3\pi)/(10))=\cos ((8\pi)/(10))`

We can simplify it by two:

`\cos ((8\pi)/(10))=\cos ((4\pi)/(5))`

Answer:

cos(4pi/5)