if y=tan-¹(1-x²÷1+x²)
then dy/dx is equal to
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Answer:
Given y=tan
−1
(
1+x
2
−
1−x
2
1+x
2
+
1−x
2
)
Put x
2
=cos2θ⇒θ=
2
1
cos
−1
x
2
--- (1)
=tan
−1
(
1+cos2θ−
1−cos2θ
1+cos2θ
+
1−cos2θ
)
⇒tan
−1
(
2
cosθ−
2
sinθ
2
cosθ+
2
sinθ
)
⇒tan
−1
(
1−tanθ
1+tanθ
)
⇒tan
−1
⎝
⎛
1−tan(
4
π
)tanθ
tan(
4
π
+tanθ)
⎠
⎞
⇒tan
−1
tan(
4
π
+θ)=
4
π
+θ
⇒y=
4
π
+
2
1
cos
−1
x
2
dx
dy
=0−
2
1
×
1−x
4
1
×2x=−
1−x
4
x
Step-by-step explanation:
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