Important Trigonometric Formulas ~ Learners Encyclopedia

1. Sin (90 – A) = Cos A

3. Cos (90 – A) = Sin A

5. Tan (90 – A) = Cot A

7. Cot (90 – A) = Tan A

2. Sin (90 + A) = Cos A

4.Cos (90 + A) = – SinA

6.Tan (90 + A)= – Cot A

8.Cot (90 + A)= – Tan A

9. Sin (A ± B) = Sin A. Cos B ± Cos A. Sin B
10. Cos (A ± B) = Cos A. Cos B ∓ Sin A. Sin B

11. Tan (A ± B) = Tan A ± Tan B 12. Cot (A ± B) = 1 ∓ Cot A. Cot B

1 ∓ Tan A. Tan B Cot A ± Cot B

13. Sin (A + B)(A – B) = Sin² A – Cos² B or Cos ² A – Cos²B

14. Cos (A – B)(A + B) = Cos² A – Sin² B

15.2Sin A.Cos B = Sin(A + B) + Sin(A – B) 16.2Cos A.Sin B = Sin(A + B) - Sin(A – B)

17.2Cos A.Cos B = Cos(A + B)+Cos(A – B) 18. 2Sin A.Cos B = Cos(A+B) - Cos(A– B)

19. Sin C+Sin D = 2 Sin C + D .Cos C – D 20. Sin C – Sin D = 2 Sin C – D Cos C + D

2 2 2 2

21. Cos C+Cos D = 2 Cos C + D. Cos C – D 22. Cos C–Cos D= - 2 Sin C+D. Sin C – D

2 2 2 2

23. Sin 2A = 2 Sin A. Cos A 24. Cos 2A = Cos² A – Sin² A

25. Cos 2A = 2Cos²A – 1 or 1 – 2Sin² A 26. Tan 2A = 2 Tan A

1 – Tan² A

27. Sin 2A = 2 Tan A 28. Cos 2A = 1 – Tan² A

1 + Tan² A 1 + Tan² A

29. Sin3A = 3SinA – 4Sin³ A 30.Tan 3A = 3Tan A – Tan³

31. Cos3A = 4Cos³A – 3CosA 1 – 3 Tan³ A

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