Question

If \(\sin A = \dfrac{15}{17}\) and \(\sin B = \dfrac{7}{25}\) , then sin (A - B) =?

A. \(\dfrac{304}{425}\)

B. \(\dfrac{416}{425}\)

C. \(\dfrac{297}{425}\)

D. \(\dfrac{87}{425}\)

1. A
2. C
3. D
4. B

Answer 1

Correct Answer - Option 1 : A

Given:

\(\sin A = \dfrac{15}{17}\) and \(\sin B = \dfrac{7}{25}\)

Formula used:

sin(A - B) = sinAcosB - cosAsinB

Calculation:

\(\sin A = \dfrac{15}{17}\), then \(\cos A = \dfrac{8}{17}\)

\(\sin B = \dfrac{7}{25}\), then \(\cos B = \dfrac{24}{25}\)

sin(A - B) = sinAcosB - cosAsinB

⇒ (15/17) × (24/25) - (8/17) × (7/25)

⇒ (72/85) - (56/425)

⇒ (360 - 56)/425

⇒ 304/425

∴ The value of sin(A - B) is 304/425.