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```
proof of compound angles

```
6 years ago

```							COS(A-B)=COSA.COSB+SINA.SINB
1.COS(A-B)
Let X`OX AND YOY` be the coordinate axes.Consider a unit circle with O as the centre.
Let p1,p2 and p3 be the three points on the circle such that angleXOP1=A,angleXOP2=B and angle XOP3=A-B.
As we know that the terminal side of any angle intersects the circle with centre at O and unit radius at a point whose coordinates are the cosine and sine of angle.
Chordp0p3=Chordp1p2
```
6 years ago
```							SIN(A-B)=SINACOSB-COSASINB
SIN(A-B)=COS(90-(A-B))
= COS(90-A)+B)
= COS(90-A)COSB-SIN(90-A)SINB
= SINACOSB-COSASINB
SIN(A+B)=SIN(A-(-B))
=SINA COS(-B)-COSA SIN(-B)
=SINA COSB+COSA SINB
```
6 years ago
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