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  4. If sin -1( sin 5)+ cos -1( cos 10)+ tan -1( tan (-6))+ cot -1( cot (-10))=a π+b then (a-b) equals

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Q. If $\sin ^{-1}(\sin 5)+\cos ^{-1}(\cos 10)+\tan ^{-1}(\tan (-6))+\cot ^{-1}(\cot (-10))=a \pi+b$ then $(a-b)$ equals

Inverse Trigonometric Functions

Solution:

$a \pi+ b =8 \pi-21$.