Q61 / 160 · AP EAMCET 2024 (20 May Shift 1) · Mathematics

$\frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}=$

  • A
    $\tan 35^{\circ}$
  • Correct answer
    B
    $\tan 55^{\circ}$
  • C
    $\tan 20^{\circ}$
  • D
    $\tan 70^{\circ}$

Solution

$\frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}=\frac{\cos \left(\frac{10+80}{2}\right)^{\circ} \cos \left(\frac{10-80}{2}\right)^{\circ}}{\cos \left(\frac{10+80}{2}\right)^{\circ} \sin \left(\frac{10-80}{2}\right)^{\circ}}$ $=\frac{\cos 35^{\circ}}{\sin 35^{\circ}}=\cot 35^{\circ}=\tan 55^{\circ}$

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

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