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Question

ddxcsc1(1+x22x) is equal to

A
2(1+x2),x0
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B
2(1+x2),x0
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C
2(1x2)(1+x2)|1x2|,x±1,0
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D
None of the above
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Solution

The correct option is B 2(1x2)(1+x2)|1x2|,x±1,0
ddxcsc1(1+x22x)=ddxsin1(2x1+x2)
=11(2x1+x2)2((1+x2)2(2x)(2x)(1+x2)2)
=2(1x2)(1+x2)|1x2|, x±1,0

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