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Question

Inverse circular functions,Principal values of sin1x,cos1x,tan1x.
tan1x+tan1y=tan1x+y1xy, xy<1
π+tan1x+y1xy, xy>1.
Evaluate the following :
(a) sin[π3sin1(12)]
(b) sin[π2sin1(32)]

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Solution

(a) sin[π3sin1(12)]
=sin[π3+sin1(12)]=sin(π3+π6)=sinπ2=1
sin1(x)=sin1x..
(b) Just as part (a).
sin(π2+π3)=cosπ3=12

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