In this post I’ll be demonstrating how one can prove that sin(A-B)=sin(A)cos(B)-cos(A)sin(B) geometrically…

First of all, let me show you this diagram…

**sin(A-B)=sin(A)cos(B)-cos(A)sin(B) proof**

**If you click on the diagram, you will be able to see its full size version.*

**IMPORTANT FACTS ABOUT THE DIAGRAM**

Now, to begin with, I will have to write about some of the properties related to the diagram…

**Property 1:**

Angle B + (A – B) = B + A – B = A

Therefore, angle POR = A.

**Property 2:**

Angle OPS = 90 degrees

**Property 3:**

Length OS = 1

**Also note:**

All angles within a triangle on a flat plane should add up to 180 degrees. If you understand this rule, you will be able to discover why the angles shown on the diagram are correct. Angles which are 90 degrees are shown on the diagram too.

**PROVING THAT SIN(A-B)=SIN(A)COS(B)-COS(A)SIN(B)**

Since I’ve noted down some of the important properties related to the diagram, I can now focus on demonstrating why the formula above is true. I will demonstrate why the formula above is true using mathematics and the SOH CAH TOA rule…

But it turns out that…

Because:

Now, what is PR and what is PQ?

And finally, to sum it all up:

**Need a better explanation? Watch this video…**

**Related Videos:**

**https://www.youtube.com/watch?v=4K6xr8hjkTw**[sin(A+B)=sin(A)cos(B)+cos(A)sin(B) proof – geometrical]**https://www.youtube.com/watch?v=-n6h6-CT0-0**[cos(A+B)=cos(A)cos(B)-sin(A)sin(B) proof – geometrical]**https://www.youtube.com/watch?v=gDOGT6NcD60**[cos(A-B)=cos(A)cos(B)+sin(A)sin(B) proof – geometrical]**The trigonometric identity playlist**

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Simple But Elegant Way To Prove That sin(A+B)=sinAcosB+cosAsinB (Edexcel Proof Simplified)

This tutorial is very straight forward and helpful. I’m really thankful for this. I’ve been searching around for ways to do this. I actually got how to prove cos(A+B) and sin(A+B).

However, cos(A-B) and sin(A-B) have been giving me problems. Thanks to this tutorial, I finally understand it. I also watched your video and subscribed to your channel. Hope to see more soon.

Thank you Soneye. I wish you the best of luck with your blogging and studying. Kind regards, Tiago.

I read the whole article and watched the video, it really helped me. The diagram and properties are what we can use to prove it geometrically. Is there any other methods that I can use?. Thanks in advance. Page bookmarked