Question

If $tan\theta =cot\theta$ and $0^{\circ }\le \theta \le {90}^{\circ }$, state the value of $\theta$

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

$tan\theta =cot\theta$
$tan\theta =\frac{1}{tan\theta }$
$ta{n}^2\theta =1$
$tan\theta =\pm 1$
Value of $tan\theta$ is positive in first quadrant.
Neglect the negative value as $\theta$ is acute.
$tan\theta =1$
$tan\theta =tan{45}^o$
$\Rightarrow \theta ={45}^{\circ }$