prove ...................
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2tan-¹(1+x/1-x)+sin-¹(1-x²/1+x²)
put x=tan@
then@=tan-¹(x)
now 2tan-¹(1+tan@/1-tan@)+sin-¹(1-tan²@/1+tan²@)
2tan-¹(tan(π/4+@)]+sin-1(cos2@)
=2(π/4+@)+sin-¹(sin(π/2-2@)
=π/2+2@+π/2-2@=2π/2=π
put x=tan@
then@=tan-¹(x)
now 2tan-¹(1+tan@/1-tan@)+sin-¹(1-tan²@/1+tan²@)
2tan-¹(tan(π/4+@)]+sin-1(cos2@)
=2(π/4+@)+sin-¹(sin(π/2-2@)
=π/2+2@+π/2-2@=2π/2=π
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