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Railways PYQCBT 1 2016

RRB NTPC · Question 29

If \(\tan A = \frac{{15}}{8}\) and \(\tan B = \frac{{7}}{24}\), then cos(A + B) = ? A. \(\frac{{87}}{{425}}\) B. \(\frac{{304}}{{425}}\) C. \(\frac{{297}}{{425}}\) D. \(\frac{{416}}{{425}}\)

  1. A

  2. C

  3. B

  4. D

Show answer & explanation

Answer: (A) A

Explanation

tan A = 15/8 gives sin A = 15/17, cos A = 8/17; tan B = 7/24 gives sin B = 7/25, cos B = 24/25. cos(A + B) = cos A cos B − sin A sin B = (192 − 105)/425 = 87/425.