The value of cos − 1 ( tan ( 4 7 π ) ) is, 4 π , 2 π , π, 3 2 π

cos − 1 ( tan 4 7 π ) = cos − 1 tan ( 2 π − 4 π ) = cos − 1 ( − tan 4 π ) = cos − 1 ( − 1 ) = π

The value of cos − 1 ( tan ( 4 7 π ) ) is

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The value of $\cos ^{-1}\left(\tan \left(\frac{7 \pi}{4}\right)\right)$ is

MathematicsTrigonometric EquationsMHT CETMHT CET 2022 (07 Aug Shift 2)

Options:

A $\frac{\pi}{4}$
B $\frac{\pi}{2}$
C $\pi$
D $\frac{2 \pi}{3}$

Solution:

1481 Upvotes Verified Answer

The correct answer is: $\pi$

$\begin{aligned} & \cos ^{-1}\left(\tan \frac{7 \pi}{4}\right)=\cos ^{-1} \tan \left(2 \pi-\frac{\pi}{4}\right)=\cos -1\left(-\tan \frac{\pi}{4}\right) \\ & =\cos ^{-1}(-1) \\ & =\pi\end{aligned}$

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