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Question

In ABC, if sin2A=sin2B but AB and 3tanA4=0, then value of expression 11+tan2B+sin(BA)2+cotC(cosB1+sin2AcosA1+sin2B) is

A
34
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B
12
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C
14
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D
0
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Solution

The correct option is B 12
sin2A=sin2B=sin(π2B)2A=π2BA+B=π2C=π2
Given that tanA=43
Then sinA=45,cosA=35B=π2AsinB=35,cosB=45
Now putting all the values in the expression we have the expression as
11+916+sinBcosAcosBsinA2+0=1625+12(35.3545.45)=12

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