1. ## [solved] inverse trig functions

let x be a positive number and let theta= tan^-1 x

a) simplify tan ( pi/2 - theta)
b) show that tan^-1 (1/x) = (pi/2) - theta

Thanks

Do i have to expand the tan function?

Nvm i got it. Its just a complimentary angle. so cot theta.

2. $\tan{\theta} = x$.

$\tan{\left(\frac{\pi}{2} - \theta\right)} = \frac{\sin{\left(\frac{\pi}{2} - \theta\right)}}{\cos{\left(\frac{\pi}{2} - \theta\right)}}$

$= \frac{\cos{\theta}}{\sin{\theta}}$

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

$= \frac{1}{x}$.

And since $\tan{\left(\frac{\pi}{2} - \theta\right)} = \frac{1}{x}$

that means $\tan^{-1}\left(\frac{1}{x}\right) = \frac{\pi}{2} - \theta$.