Trigonometric functions

The secondary trigonometric functions are the sine and cosine of an angle. These are sometimes abbreviated sin(θ) and cos(θ), respectively, where θ is the angle, but the parentheses around the angle are often omitted, e.g., sin θ and cos θ.

When the trigonometric functions are reflected from certain angles, the result is often one of the other trigonometric functions.

Trigonometric functions are as given below

  1. $$sin (A + B) = sin A cos B + cos A sin B$$
  2. $$sin (A - B) = sinA cosB - cos A sin B$$
  3. $$cos (A + B) = cos A cos B - sin A sin B$$
  4. $$cos (A - B) = cos A cos B + sin A sin B$$
  5. $$tan (A + B) = {tan A + tan B \over 1 - tan A tanh B}.$$
  6. $$tan (A - B) = {tan A - tan B \over 1 + tan A tanh B}.$$
  7. $$sin (A + B) sin (A - B) = sin^2A - sin^2B$$
  8. $$cos (A + B) cos (A - B) = cos^2 A - sin^2 B$$
  9. $$2sin A cos B = sin (A + B) + sin (A - B)$$
  10. $$2cos A sin B = sin (A + B) - sin (A - B)$$
  11. $$2cos A cos B = cos (A + B) + cos (A - B)$$
  12. $$2sin A sin B = cos (A - B) - cos (A + B)$$
  13. $$ sin C + sin D = 2sin ({C + D \over 2}) cos ({C - D \over 2})$$
  14. $$sin C - sin D = 2cos ({C + D \over 2}) sin ({C - D \over 2})$$
  15. $$cos C - cos D = 2cos ({C + D \over 2}) cos ({C - D \over 2})$$
  16. $$cos C - cos D = - 2sin ({C + D \over 2}) sin ({C - D \over 2})...... (C > D) $$
    OR
    $$cos C - cos D = - 2sin ({C + D \over 2}) sin ({D - C \over 2})...... (C < D) $$
  17. $$ sin ({π\over 2} - θ) = cos θ $$
  18. $$tan ({π\over 2} + θ) = - cot θ $$
  19. $$cos ({π\over 2} - θ) = sin θ $$
  20. $$cot ({π\over 2} - θ) = - tan θ $$
  21. $$cosec ({π\over 2} - θ) = sec θ $$
  22. $$sec ({π\over 2} - θ) = cosec θ $$
  23. $$tan ({π\over 2} - θ) = cot θ $$
  24. $$cot ({π\over 2} - θ) = tan θ $$
  25. $$sin ({π\over 2} + θ) = cos θ $$
  26. $$cos ({π\over 2} + θ) = - sin θ $$
  27. $$cosec ({π\over 2} + θ) = sec θ $$
  28. $$sec ({π\over 2} + θ) = - cosec θ $$

Labels: MPSC, TET, NET-SET, Maths, Mathamatics, Trignometric Functions


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