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Question : 65 of 160
Marks:
+1,
-0
Solution:
Consider the equation.
y=tan−1x{} +sin{2tan−1√} Substitute
cos‌2‌θ for
x in the above equation.
y=tan−1{ } +sin{2tan−1√| 1−cos‌2‌θ |
| 1+cos‌2‌θ |
} =tan−1{| cos‌2‌θ |
| 1+sin‌2‌θ |
}+sin{2tan−1√} =tan−1{| cos2θ−sin2θ |
| (cos‌θ+sin‌θ)2 |
} +sin{2tan−1(tan‌θ)} =tan−1{| cos‌θ−sin‌θ |
| (cos‌θ+sin‌θ) |
}+sin{2θ} Solve further,
y=tan−1{ }+sin‌2‌θ y=tan−1(tan(−θ))+sin‌2‌θ =−θ+sin‌2‌θ =−cos−1x+√1−x2 Differentiate both side with respect to
x.
=. +(−2x) =
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