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Question

If cosecA+cotA=11/2, then tanA=?


A

21/22

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B

15/16

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C

44/117

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D

117/43

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Solution

The correct option is C

44/117


The explanation for the correct option:

Step 1. Using the identity cosec2Acot2A=1,

Given, cosecA+cotA=11/2.(i)

(cosecA+cotA)(cosecAcotA)=1(11/2)(cosecAcotA)=1cosecAcotA=2/11.(ii)

Step 2. Subtracting (ii) from (i),

cosecA+cotAcosecA+cotA=(11/2)(2/11)2cotA=(1214)22cotA=117/44tanA=1cotA=44117

Hence, The correct answer is option (C).


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