Math Doubts

Cos angle sum identity

Expansion form

$\cos{(A+B)}$ $\,=\,$ $\cos{A}\cos{B}$ $-$ $\sin{A}\sin{B}$

Simplified form

$\cos{A}\cos{B}$ $-$ $\sin{A}\sin{B}$ $\,=\,$ $\cos{(A+B)}$

Introduction

The angle sum identity for the cosine function is generally called as cos of sum of two angles or cos of compound angle identity. It’s used as a trigonometric formula in two cases.

  1. To expand cos of sum of two angles as the subtraction of product of cosines of angles from product of sines of angles.
  2. To simplify the subtraction of products of cosines of angles from products of sines of angles as cos of compound angle function.

Formula

The angle sum cos formula is written in several ways in mathematics. For example, $\cos{(A+B)}$, $\cos{(x+y)}$, $\cos{(\alpha+\beta)}$, and so on.

$(1) \,\,\,\,\,\,$ $\cos{(A+B)}$ $\,=\,$ $\cos{A}\cos{B}$ $-$ $\sin{A}\sin{B}$

$(2) \,\,\,\,\,\,$ $\cos{(x+y)}$ $\,=\,$ $\cos{x}\cos{y}$ $-$ $\sin{x}\sin{y}$

$(3) \,\,\,\,\,\,$ $\cos{(\alpha+\beta)}$ $\,=\,$ $\cos{\alpha}\cos{\beta}$ $-$ $\sin{\alpha}\sin{\beta}$

Proof

Now, let’s learn how to derive the angle sum cos identity in mathematical form in trigonometry by geometrical method.



Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more