tan^-1(cosx/1+sinx)=π/4-x/2
Answers
Answered by
2
tan-1[cosx / (1+sinx)]
=tan-1[ sin(pi/2 - x) / (1+cos(pi/2 - x))]
Let t=pi/2-x
=tan-1[ sint / (1+cost)]
=tan-1[2sin(t/2) cos(t/2) / (2 cos2(t/2))] {since sin2x=2sinx cosx and 1+cos2x=2cos2x }
=tan-1[sin(t/2)/cos(t/2)]
=tan-1[tan(t/2)]
=t/2
=(pi/2 - x)/2
=pi/4 - x/2
Hence Proved.
Similar questions