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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.
Using the principal values, express the following as a single angle :
3tan1(12)+2tan1(15)+sin1142655.

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Solution

sin1xa=tan1x(a2x2)
T3=tan114231
2tan1x=tan12x1x2
T2=tan1512
3tan1x=tan13xx313x2
T1=tan1112
E=tan1112+tan1512+tan114231
=π+tan1112+51215524+tan114231
Here ab>1 and hence π+tan1()
=πtan114231+tan114231=π.

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