Question

cot inverse tan pi by 7 ​

Answer 1

Answer:

${cot}^{ - 1} (tan \: \frac{ \pi}{7} ) \\ \\ \implies \: {cot}^{ - 1} \bigg( \: cot( \frac{ \pi}{2} - \frac{ \pi}{7} ) \bigg) \\ \\ \implies \: \frac{ \pi}{2} - \frac{ \pi}{7} \\ \\ \implies \: \frac{5 \pi}{14} \: \\ \\ this \: is \: the \: required \: solution$

Answer 2

Question: The value of the function $cot^{-1}tan\left(\frac{\pi}{7}\right)$.

Answer:

The value of the trigonometric function $cot^{-1}tan\left(\frac{\pi}{7}\right)$ is $\frac{5\pi}{14}$.

Step-by-step explanation:

Some inverse trigonometric identities are:-

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

(ii) $tan^{-1}(tanx)=x$

Step 1 of 1

To find:-

The value of the trigonometric function $cot^{-1}\left(tan\left(\frac{\pi}{7}\right)\right)$.

Consider the given trigonometric function as follows:

$cot^{-1}\left(tan\left(\frac{\pi}{7}\right)\right)$ _____ (1)

Here, let us assume $x=tan\frac{\pi}{7}$.

Then,

From identity (i), we have

$cot^{-1}x=\frac{\pi}{2}-tan^{-1}x$

Substitute the value of $cot^{-1}x$ in the function (1) as follows:

⇒ $\frac{\pi}{2}-tan^{-1}\left(tan\left(\frac{\pi}{7}\right)\right)$

Now,

Using the identity (ii), we get

⇒ $\frac{\pi}{2}-\frac{\pi}{7}$

Lastly, apply the difference operation to simplify the function as follows:

⇒ $\frac{7\pi - 2\pi}{14}$

⇒ $\frac{5\pi}{14}$

Final answer: The value of the trigonometric function $cot^{-1}tan\left(\frac{\pi}{7}\right)$ is $\frac{5\pi}{14}$.

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