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Q.

If 0<θ<π2,and  ify+11−y=1+sinθ1−sinθ,then  y  is  equal to

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a

cotθ2

b

tanθ2

c

cotθ2+tanθ2

d

cotθ2−tanθ2

answer is B.

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Detailed Solution

y+11−y=1+sinθ1−sinθ y+11−y=(cosθ2+sinθ2)2(cosθ2−sinθ2)2 y+11−y=cosθ2+sinθ2|cosθ2−sinθ2| y+11−y=cosθ2+sinθ2cosθ2−sinθ2          [∵0<θ<π2⇒0<θ2<π4                   ⇒cosθ2>sinθ2] y+11−y=1+tanθ21−tanθ2⇒y=tanθ2
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