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Question

If 2tan1(cosx)=tan1(2cosecx), then sinx+cosx=

A
22
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B
2
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C
12
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D
12
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Solution

The correct option is C 2
tan1(A)+tan1(B)=tan1(A+B1AB)
2tan1(cosx)=tan1(2cosecx)
tan1(2cosx1cos2x)=tan1(2sinx) (tan1(A)+tan1(B)=tan1(A+B1AB))
2cosxsin2x=2sinx
cosx=sinx
x=45
cosx+sinx=2sinx=2sin(45)=2×12=2

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