All necessary trigonometry laws [part-1]

Here I will Post 4 part of this laws and total laws will 40. In first part, I am going to share 10 laws. In second part, I will share 8 laws. In third part, I will share 12 laws and the last part will contain 10 laws.
However, I am sharing today's 10 laws.

1. sin(A + B) = sinA.cosB + cosA.sinB
2. sin(A - B) = sinA.cosB - cosA.sinB
3. cos(A + B) = cosA.cosB - sinA.sinB
4. cos(A - B) = cosA.cosB + sinA.sinB
5. tan(A + B) = ^{tanA + tanB}_{1 - tanA.tanB}
6. tan(A - B) = ^{tanA - tanB}_{1 + tanA.tanB}
7. cot(A + B) = ^{cotA.cotB - 1}_{cotA + cotB}
8. cot(A - B) = ^{cotA.cotB + 1}_{cotB - cotA}
9. sin(A + B).sin(A - B) = sin²A - sin²B = cos²B - cos²A
10. cos(A + B).cos(A - B) = cos²A - sin²B = cos²B - sin²A

Okey, I will try to come back as soon as possible to share my sencond part.