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CBSE Class 12 Math 2013 Solved Paper

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Question : 2
Total: 29
Write the value of tan (2tan−1
1
5
)
Solution:  
We know: 2 tan−1x = tan−1
2x
1−x2
⇒ 2tan−1
1
5
 = tan−1
2(
1
5
)
1−(
1
5
)2
 = tan−1
2
5
24
25
 = tan−1
5
12
∴ tan (2tan−1
1
5
) = tan (tan−1
5
12
) =
5
12
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