Question

If Sin A : Cos A = 4 : 7 , then the value of \(\frac{(7sinA−3cosA)}{(7sinA+2cosA)}\) is 

• A. \(\frac{3}{14}\)
• B. \(\frac{3}{2}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{1}{6}\)

Answer 1

The Correct Option is D

Assume \(sin A = 4 and\ cos A = 7\)

The expression given in the question, = \(\frac{7\ sin A - 3\ cos A}{7\ sin A + 2\ cos A}\)

From the equation we get = \(\frac{7(4) - 3(7)}{7(4) + 2(7)}\)

= \(\frac{7}{42}\) = \(\frac{1}{6}\)

The correct option is (D): \(\frac{1}{6}\)