Find x if Sin^-1 = tan^-1 x
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Answer:
tan
−1
x=
2
π
−sin
−1
x
tan
−1
x=cos
−1
x
tan
−1
x=tan
−1
x
1−x
2
x=
x
1−x
2
x
2
=
1−x
2
On squaring both sides
x
4
=1−x
2
x
4
−x
2
−1=0
x
2
=
2
−1±
1+4
There are two possibilities solution -ve and +ve
When -ve taken x
2
=
2
−1−
5
When +ve taken x
2
=
2
−1+
5
2x
2
=
5
−1
Hence proved
Step-by-step explanation:
tan
−1
x=
2
π
−sin
−1
x
tan
−1
x=cos
−1
x
tan
−1
x=tan
−1
x
1−x
2
x=
x
1−x
2
x
2
=
1−x
2
On squaring both sides
x
4
=1−x
2
x
4
−x
2
−1=0
x
2
=
2
−1±
1+4
There are two possibilities solution -ve and +ve
When -ve taken x
2
=
2
−1−
5
When +ve taken x
2
=
2
−1+
5
2x
2
=
5
−1
Hence proved
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