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Mathematics
Mathematics
Problem
Assertion:
Statement I
Derivative of
sin
−
1
(
2
x
1
+
x
2
)
\sin^{-1}\left(\frac{2x}{1+x^2}\right)
sin
−
1
(
1
+
x
2
2
x
)
w.r.t.
cos
−
1
(
1
−
x
2
1
+
x
2
)
\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)
cos
−
1
(
1
+
x
2
1
−
x
2
)
is 1 for
0
<
x
<
1
0 < x < 1
0
<
x
<
1
. Reason:
Statement II
sin
−
1
(
2
x
1
+
x
2
)
=
cos
−
1
(
1
−
x
2
1
+
x
2
)
\sin^{-1}\left(\frac{2x}{1+x^2}\right) = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)
sin
−
1
(
1
+
x
2
2
x
)
=
cos
−
1
(
1
+
x
2
1
−
x
2
)
for
−
1
≤
x
≤
1
-1 \le x \le 1
−
1
≤
x
≤
1
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