Trigonometric Formulas

Remember these trigonometric formulas

20 flashcards · Mathematics · by Dasp Parihar

1. What is tan2θtan2\thetatan2θ ?

   2tanθ1−tan2θ\Large\frac{2tan\theta}{1-tan^2\theta}1−tan2θ2tanθ​

2. What is sin2θsin2\thetasin2θ ?

   2sinθcosθ2sin{\theta}cos{\theta}2sinθcosθ 2tanθ1+tan2θ\Large\frac{2tan\theta}{1+tan^2\theta}1+tan2θ2tanθ​

3. What is cos2θcos2\thetacos2θ ?

   cos2θ−sin2θcos^2\theta - sin^2\thetacos2θ−sin2θ 2cos2θ−12cos^2\theta - 12cos2θ−1 1−2sin2θ1 - 2sin^2\theta1−2sin2θ 1−tan2θ1+tan2θ\Large\frac{1-tan^2\theta}{1+tan^2\theta}1+tan2θ1−tan2θ​

4. What is sin3θsin3\thetasin3θ ?

   3sinθ−4sin3θ3sin\theta - 4sin^3\theta3sinθ−4sin3θ

5. What is cos3θcos3\thetacos3θ ?

   4cos3θ−3cosθ4cos^3\theta - 3cos\theta4cos3θ−3cosθ

6. What is tan3θtan3\thetatan3θ ?

   3tanθ−tan3θ1−3tan2θ\Large\frac{3tan\theta - tan^3\theta}{1 - 3tan^2\theta}1−3tan2θ3tanθ−tan3θ​

7. What is sin(A±B)sin(A \pm B)sin(A±B) ?

   sinAcosB±cosAsinBsinAcosB \pm cosAsinBsinAcosB±cosAsinB

8. What is cos(A±B)cos(A \pm B)cos(A±B) ?

   cosAcosB∓sinAsinBcosAcosB \mp sinAsinBcosAcosB∓sinAsinB

9. What is sin(A+B)sin(A−B)sin(A + B)sin(A - B)sin(A+B)sin(A−B) ?

   sin2A−sin2Bsin^2A - sin^2Bsin2A−sin2B cos2B−cos2Acos^2B - cos^2Acos2B−cos2A

10. What is cos(A+B)cos(A−B)cos(A + B)cos(A - B)cos(A+B)cos(A−B) ?

    cos2A−sin2Bcos^2A - sin^2Bcos2A−sin2B cos2B−sin2Acos^2B - sin^2Acos2B−sin2A

11. What is tan(A±B)tan(A \pm B)tan(A±B) ?

    tanA ± tanB1 ∓ tanAtanB\Large\frac{tanA\,\pm \,tanB}{1\, \mp \,tanAtanB}1∓tanAtanBtanA±tanB​

12. What is cot(A±B)cot(A \pm B)cot(A±B) ?

    cotBcotA ∓ 1cotB ± cotA\Large\frac{cotBcotA\, \mp \,1}{cotB\,\pm \,cotA}cotB±cotAcotBcotA∓1​

13. What is sinC+sinDsinC + sinDsinC+sinD ?

    2sinC+D2cosC−D2\large 2sin\frac{C + D}{2}cos\frac{C - D}{2}2sin2C+D​cos2C−D​

14. What is sinC−sinDsinC - sinDsinC−sinD ?

    2cosC+D2sinC−D2\large 2cos\frac{C + D}{2}sin\frac{C - D}{2}2cos2C+D​sin2C−D​

15. What is cosC+cosDcosC + cosDcosC+cosD ?

    2cosC+D2cosC−D2\large 2cos\frac{C + D}{2}cos\frac{C - D}{2}2cos2C+D​cos2C−D​

16. What is cosC−cosDcosC - cosDcosC−cosD ?

    −2sinC+D2sinC−D2\large -2sin\frac{C + D}{2}sin\frac{C - D}{2}−2sin2C+D​sin2C−D​

17. What is 2sinAcosB2sinAcosB2sinAcosB ?

    sin(A+B)+sin(A−B)sin(A + B) + sin(A - B)sin(A+B)+sin(A−B)

18. What is 2cosAsinB2cosAsinB2cosAsinB ?

    sin(A+B)−sin(A−B)sin(A + B) - sin(A - B)sin(A+B)−sin(A−B)

19. What is 2cosAcosB2cosAcosB2cosAcosB ?

    cos(A+B)+cos(A−B)cos(A + B) + cos(A - B)cos(A+B)+cos(A−B)

20. What is 2sinAsinB2sinAsinB2sinAsinB ?

    cos(A−B)−cos(A+B)cos(A - B) - cos(A + B)cos(A−B)−cos(A+B)