3u can make a substitution as x=sin(theta)
and write 1=sin2(theta)/2+cos2(theta/2)
Prove that tan-1(√1+x - √1-x)/(√1+x + √1-x) = Ï€/4-1/2 Cos-1x
0<x<1.
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3 Answers
3
62Apart from what sankara said,,,...
What i was saying is this
√1+x - √1-x√1+x + √1-x = 1 - tan(1/2 cos-1x)1 + tan(1/2 cos-1x)
Now apply componendo dividendo to get
√1+x√1-x = 1 tan(1/2 cos-1x)
√1-x√1+x = tan(1/2 cos-1x)
2 tan-1(√1-x√1+x) = cos-1x
2 cos-1(√(1+x)/2 ) = cos -1x
Which has 1 step left if you take cos on both sides....
