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UPSC NDA Math Model Paper 3
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© examsnet.com
Question : 13
Total: 120
tan
(
2
tan
−
1
(
cos
x
)
)
is equal to ?
2tan x cosec x
2cot x cosec x
2cos x cosec x
cot x cosec x
Validate
Solution:
As we know,
2
tan
−
1
x
=
tan
−
1
2
x
1
−
x
2
Therefore,
2
tan
−
1
cos
x
=
tan
−
1
2
cos
x
1
−
cos
2
x
=
tan
−
1
2
cos
x
sin
2
x
=
tan
−
1
(
2
cot
x
cosec
x
)
As we know,
tan
(
tan
−
1
x
)
=
x
So,
tan
(
tan
−
1
(
2
cot
x
cosec
x
)
)
=
2
cot
x
cosec
x
© examsnet.com
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