Trigonofunction

Geometry Level 3

Determine whether the function $\text{f(x)}$ is even or odd .

$\large \text{f(x)} = \left( 1 + \tan\left(\dfrac{\pi}{3} - x\right)\right)\left(1+ \tan\left(x - \dfrac{\pi}{12}\right)\right)$

There is insufficient information Neither even nor odd Odd function Even function

1 solution

Tanishq Varshney
Sep 15, 2015

$\large{f(x)=(1+\tan \left (\frac{\pi}{3}-x \right ))(1+\tan \left (x-\frac{\pi}{3}+\frac{\pi}{4} \right) )}$

$\large{f(x)=(1+\tan \left (\frac{\pi}{3}-x \right ))(1+\frac{1+\tan \left (x-\frac{\pi}{3} \right )}{1-\tan \left (x-\frac{\pi}{3} \right )})}$

$\large{f(x)=(1+\tan \left (\frac{\pi}{3}-x \right ))\frac{2}{(1-\tan \left (x-\frac{\pi}{3} \right ))}}$

we know $\tan (-x)=-\tan (x)$

$\large{f(x)=2}$

Kudos! Nice solution.

Akhil Bansal - 5 years, 9 months ago