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  4. The value of sin -1( sin 9)+ tan -1( tan 9)+ sec 2( tan -1 2)+ operatornamecosec2( cot -1 3) is equal to

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Q. The value of $\sin ^{-1}(\sin 9)+\tan ^{-1}(\tan 9)+\sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$ \sin ^{-1}(\sin 9)+\tan ^{-1}(\tan 9)+\sec ^2\left(\tan ^{-1}2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) $
$=(3 \pi-9)+(9-3 \pi)+5+10=15$