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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(sin4)+cos−1(cos8)+tan−1(tan6)+cot−1(cot10)=a+bπ then (a+b) equals

Inverse Trigonometric Functions

Solution:

π−4+8−2π+6−2π+10−3π=20−6π
∴a=20;b=−6
⇒a+b=14.