Question

Given the identity tan x = sinx/cosx are the relationship between the sine and cosine of complementary angles what is tan 90 -a

Answer 1

Answer:

$\tan\left(\frac{\pi}{2} - x\right) = \cot x.$

Proof:

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