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  4. If sin -1( sin 4)+ cos -1( cos 8)+ tan -1( tan 6)+ cot -1( cot 10)=a+b π then (a+b) equals

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Q. If $\sin ^{-1}(\sin 4)+\cos ^{-1}(\cos 8)+\tan ^{-1}(\tan 6)+\cot ^{-1}(\cot 10)=a+b \pi$ then $(a+b)$ equals

Inverse Trigonometric Functions

Solution:

$ \pi-4+8-2 \pi+6-2 \pi+10-3 \pi=20-6 \pi $
$\therefore a=20 ; b=-6 $
$\Rightarrow a+b=14 .$