Please solve this:
Show that sin
−1
(2x
1−x
2
)=2sin
−1
x
Answers
Answered by
1
Consider, LHS= sin
−1
(2x
1−x
2
)
Put x=sinθ
∴θ=sin
−1
x
L.H.S=sin
−1
(2sinθ
1−sin
2
θ
)
=sin
−1
(2sinθ
cos
2
θ
)
=sin
−1
(2sinθcosθ)
=sin
−1
sin2θ
=2θ
=2sin
−1
x=R.H.S
Hence L.H.S=R.H.S
Hence proved.
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