---
id: 699e782f8f18cf77dfce5c1a
title: Angle Sum and Difference Formulas
challengeType: 11
videoId: cWSkoA9jshQ
dashedName: angle-sum-and-difference-formulas
---

# --description--

In this video, you will learn about the angle sum and difference formulas.

# --questions--

## --text--

What is the exact value for $\sin(105°)$?

## --answers--

$\tan(60° + 45°) = \frac{\tan(60°) + \tan(45°)}{1 - \tan(60°)\tan(45°)}$

---

$\cos(15°) = \cos(60°-45°) = \cos(60°)\cos(45°) + \sin(60°)\sin(45°) = \frac{1}{2} \cdot \frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$

---

$\sin(60°-45°) = \sin(60°)\cos(45°) - \cos(60°)\sin(45°)$

---

$\sin(60° + 45°) = \sin(60°)\cos(45°) + \cos(60°)\sin(45°) = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{1}{2} \cdot \frac{\sqrt{2}}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$

## --video-solution--

4


