Question

T cot-1 tan का मान ज्ञात करें​

Answer 1

Answer:

HINDI ME BOLIYE

Step-by-step explanation:

Answer 2

The value of $cot^{-1}(tanA)$ is $\dfrac{\pi}{2}-A$.

Step-by-step explanation:

We know that,

$\quad tan^{-1}(x)+cot^{-1}(x)=\dfrac{\pi}{2}$

Putting $x=tanA$ in the above relation, we get

$\quad tan^{-1}(tanA)+cot^{-1}(tanA)=\dfrac{\pi}{2}$

$\Rightarrow A+cot^{-1}(tanA)=\dfrac{\pi}{2}$

• since $tan^{-1}(tan\theta)=\theta$

$\Rightarrow \boxed{\bold{cot^{-1}(tanA)=\dfrac{\pi}{2}-A}}$

Let us put a few values of $A$ in degree or radian:

• When $A=\dfrac{\pi}{4}$, $cot^{-1}(tan\dfrac{\pi}{4})=\dfrac{\pi}{2}-\dfrac{\pi}{4}=\bold{\dfrac{\pi}{4}}$

• When $A=\dfrac{\pi}{2}$, $cot^{-1}(tan\dfrac{\pi}{2})=\dfrac{\pi}{2}-\dfrac{\pi}{2}=\bold{0}$

• When $A=0$, $cot^{-1}(tan0)=\dfrac{\pi}{2}-0=\bold{\dfrac{\pi}{2}}$