Question

Find the exact radian value. \\tan11\tan ^{-1} 1

Solution

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Answered 2 years ago
Answered 2 years ago
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Let tan11=y\tan^{-1}1=y. So, now we have to calculate the value of yy

y=tan11tan(y)=tan(tan11)Take tangent function both sidestany=1Simplify\begin{align*} y&=\tan^{-1}1\\ \tan(y)&=\tan\left(\tan^{-1}1\right)&\textcolor{#4257b2}{\text{Take tangent function both sides}}\\ \tan y&=1&\textcolor{#4257b2}{\text{Simplify}} \end{align*}

Since tangent of an angle is 11. So, that angle must be π4\dfrac{\pi}{4}. Because range of tangent inverse function is [π2,π2]\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]

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