Q190 / 270 · NDA 2018 (Phase 2) · Mathematics

$A$ is an angle in the fourth quadrant. If satisfies the trigonometric equation $3\left(3-\tan ^2 \mathrm{~A}-\cot \mathrm{A}\right)^2=1$. Which one of the following is a value of $A$ ?

  • Correct answer
    A
    $300^{\circ}$
  • B
    $315^{\circ}$
  • C
    $330^{\circ}$
  • D
    $345^{\circ}$

Solution

Checking through options $300^{\circ}=-60^{\circ}$ So, $3\left[3-\tan ^2\left(-60^{\circ}\right)-\cot \left(-60^{\circ}\right)\right]^2$ $=3\left[3-3+\frac{1}{\sqrt{3}}\right]^2=3 \times \frac{1}{3}=1$

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

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