If cos(A−B)−cos(A+B)=x, then the value of x is
- A2sinAsinB
- B2cosAcosB
- C2cosAsinB
- D2sinAcosB
Solution & Step-by-step Explanation
Using standard trigonometric product-to-sum identities:
cos(A−B)=cosAcosB+sinAsinB
cos(A+B)=cosAcosB−sinAsinB
Subtracting the second equation from the first:
cos(A−B)−cos(A+B)=(cosAcosB+sinAsinB)−(cosAcosB−sinAsinB)
x=2sinAsinB
cos(A−B)=cosAcosB+sinAsinB
cos(A+B)=cosAcosB−sinAsinB
Subtracting the second equation from the first:
cos(A−B)−cos(A+B)=(cosAcosB+sinAsinB)−(cosAcosB−sinAsinB)
x=2sinAsinB