Question

Convert the following to simplest form cot (21pi/2-theta) ​

Answer 1

Answer:

tan thetha

Step-by-step explanation:

hope this helps!!

Answer 2

Answer:

Required value is $\tan(\theta)$

Step-by-step explanation:

Given,

$\cot( \frac{21\pi}{2} - \theta)$

Here $\frac{21\pi}{2} = 10\pi + \frac{\pi}{2}$

So,

$\cot( \frac{21\pi}{2} - \theta) = \cot(10\pi + \frac{\pi}{2} - \theta) ......(1)$

We know,

$\cot(a\pi + x) = \cot(x)$

From (1),

$\cot(10\pi + \frac{\pi}{2} - \theta) = \cot( \frac{\pi}{2} - \theta) = \tan(\theta)$

Here applied formula,

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

Some other important formulas of Trigonometry,

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