Write the value
Question:

Write the value of $\cos ^{-1}\left(\cos 1540^{\circ}\right)$

Solution:

We know that

$\cos ^{-1}(\cos x)=x$

Now,

$\cos ^{-1}\left(\cos 1540^{\circ}\right)=\cos ^{-1}\left\{\cos \left(1440+100^{\circ}\right)\right\}$

$=\cos ^{-1}\left\{\cos \left(100^{\circ}\right)\right\} \quad\left[\because \cos \left(4 \pi+100^{\circ}\right)=\cos 100^{\circ}\right]$

$=100^{\circ}$

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