Question

Solve the equation: 2 tan theta -cot theta=-1

Answer 1

The solutions are:  $\theta = 26.565^{\circ}$ and $\theta = -45^{\circ}$

Solution:

Given that,

We have to solve:

$2\ tan\ \theta - cot\ \theta = -1$

$We\ know,$

$cot\ \theta = \frac{1}{tan\ \theta}$

$Therefore \\\\2\ tan\ \theta - \frac{1}{tan\ \theta } = -1\\\\2\ tan^2 \theta - 1 = -tan\ \theta\\\\2\ tan^2 \theta + tan\ \theta - 1 = 0\\\\(2tan\ \theta - 1)(tan\ \theta + 1) = 0$

$Thus\ solutions\ are \\\\2tan\ \theta - 1 = 0 \\\\2tan\ \theta = 1 \\\\tan\ \theta = \frac{1}{2} \\\\\theta = tan^{-1} \frac{1}{2}\\\\\theta = 26.565^{\circ} \\\\And \\\\tan\ \theta + 1 = 0 \\\\tan\ \theta = -1 \\\\\theta = tan^{-1} -1\\\\\theta = -45^{\circ}$

Thus the solutions are:  $\theta = 26.565^{\circ}$ and $\theta = -45^{\circ}$

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