All necessary trigonometry laws [part-3]

Hey guys, how are you? Fine? Then I can start my 3^rd part. This is the third part of "All necessary trigonometry laws". In first part, I write 10 laws. Second part I have added 8 laws. If you missed or forget them you can view it again here.

All necessary trigonometry laws (part-1).

All necessary trigonometry laws (part-2).

In this part we will see important twelve laws. If you know this laws, then you will able to solve any hard trigonometry math. Okey let's go and see today's 12 laws.

1. sin2A = 2sinA.cosA
2. cos2A = cos²A - sin²A = 1 - 2sin²A = 2cos²A - 1
   
3. 1 - cos2A = 2cos²A
4. 1 + cos2A = 2sin²A
5. sin2A = ^2sinA_{1 + tan²A}
6. cos2A = ^{1 - tan2A}_{1 + tan²A}
7. tan2A = ^2sinA_{1 - tan²A}
8. sin3A = 3sinA - 4sin³A
9. cos3A = 4cos³A - 3cosA
10. tan3A = ^{3tanA - tan3A}_{1 - 3tan²A}
11. 4sin³A = 3sinA - sin3A
12. 4cos³A = 3cosA + cos3A

View this laws carefully and practice it yourself and wait for last part. I will come back with last part as soon as possible. Now I say Good bye.