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Let f(x) = {:{( sin x +cos x, 0 lt x lt...

` Let f(x) = {:{( sin x +cos x, 0 lt x lt (pi)/(2) ),( a, x = pi//2) , ( tan ^(2) x + cosecx , pi//2lt xlt pi ):}` then its odd extension is

A

`{:{(-tan^(2)x-cosec",",-pi lt x lt - pi/2),(-a",",x= - pi//2),(-sin x + cos x",",-pi//2 lt x lt 0):}`

B

`{:{(tan x^(2)+cosec"," ,-pi lt x lt - pi/2),(-a",",x = - pi//2),(sin x - cos x",",-pi//2 lt x lt 0):}`

C

`{:{(-tanx^(2)+cosecx",",-pi lt x lt - pi/2),(+a",",x = - pi//2),(sin x - cos x",",-pi//2 lt x lt0):}`

D

`{:{(tanx^(2)+cos x",",-pi lt x lt - pi/2),(-a",",x = - pi//2),(sin x + cos x",",- pi//2 lt x lt 0):}`

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The correct Answer is:
B
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