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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 31
Total: 50
The simplest form of tan−1[‌
√1+x−√1−x
√1+x+√1−x
] is
Solution:     👈: Video Solution
Explanation: We have,
tan−1(‌
√1+x−√1−x
√1+x+√1−x
)

Put x=cos‌2‌θ, so that θ=‌
1
2
cos−1x
tan−1(‌
√1+cos‌2‌θ−√1−cos‌2‌θ
√1+cos‌2‌θ+√1−cos‌2‌θ
)
=tan−1(‌
√2cos2θ−√2sin‌2θ
√2cos2θ+√2sin‌2θ
)
=tan−1(‌
cos‌θ−sin‌θ
cos‌θ+sin‌θ
)
=tan−1(‌
1−tan‌θ
1+tan‌θ
)
=tan−1(1)−tan−1(tan‌θ)
=tan−1(tan4)−θ
=‌
π
4
−‌
1
2
cos−1x
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