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UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions
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© examsnet.com
Question : 13
Total: 107
If cos θ =
1
√
5
, where 0 < θ <
π
2
, then
2
t
a
n
θ
1
−
t
a
n
2
θ
is equal to
[2018 CDS-II]
4/3
- 4/3
1/3
- 2/3
Validate
Solution:
2
tan
θ
1
−
tan
2
θ
=
tan
2
θ
=
sin
2
θ
cos
2
θ
sin
θ
=
√
1
−
cos
2
θ
=
√
1
−
1
5
=
2
√
5
sin
2
θ
=
2
sin
θ
cos
θ
=
2
×
2
√
5
×
1
√
5
=
4
5
cos
2
θ
=
cos
2
θ
−
sin
2
θ
=
1
5
−
4
5
=
−
3
5
2
tan
θ
1
−
tan
2
θ
=
tan
2
θ
=
sin
2
θ
cos
2
θ
=
4
5
−
3
5
=
−
4
3
© examsnet.com
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