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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.
4tan115tan1170+tan1199=π4

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Solution

2tan115=tan12/51(1/25)=tan1512.
4tan115=2tan1512
tan12(5/12)1(25/144)=tan1120119.
L.H.S.=tan1120119(tan1170tan1199)
=tan1120119tan11/701/991+(1+99)(1/70)
=tan1120119tan1296931
=tan1120119tan11239
=tan1120/1191/2391+(120/119).(1/239)
=tan1120.239119119.239+120
=tan1119.239+(239+119)119.239+120
=tan11=π/4
writing 120x=(119+1)x

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