Q66 / 180 · COMEDK 2017 · Mathematics

The value of $\cos \left(35^{\circ}+A\right) \cos \left(35^{\circ}-B\right)$ $+\sin \left(35^{\circ}+A\right) \sin \left(35^{\circ}-B\right)$ is equal to

  • A
    $\sin (A+B) \quad$
  • B
    $\sin (A-B)$
  • Correct answer
    C
    $\cos (A+B) \quad$
  • D
    $\cos (A-B)$

Solution

$\cos \left(35^{\circ}+A\right) \cos \left(35^{\circ}-B\right) +\sin \left(35^{\circ}+A\right) \sin \left(35^{\circ}-B\right)$ $=\cos \left[\left(35^{\circ}+A\right)-\left(35^{\circ}-B\right)\right]$ $=\cos (A+B)$

Hence, the correct answer is option: 'C'.

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