RRB Group D Model Paper 8 with solutions

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Question : 51 of 100

Marks: +1, -0

√{{1 + sin θ} /{1 – sin θ}}

+

√{{1 – sin θ}/ {1 + sin θ}}

is equal to

2 cos θ
2 sin θ
2 cot θ
2 sec θ

Solution:

(4)

√{{1 + sin θ} /{1 – sin θ}}

+

√{{1 – sin θ}/ {1 + sin θ}}

=

√{({1 + sin θ}) ^2/{1 – sin^2θ}}

+

√{({1 – sin θ})^2/ {1 - sin^2 θ}}

( by rationalisation)
=

√{({1 + sin θ}) ^2/{cos^2θ}}

+

√{({1 – sin θ})^2/ {cos^2 θ}}

=

{({1 + sin θ}) /{cosθ}}

+

{({1 – sin θ})/ {cos θ}}

=

2/{cosθ}

= 2 sec θ

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