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Question

# Match the columnList IList IIA. Range of f(x)=sin−1x+cos−1x+cot−1x is1.[0,π2)∪(π2,π]B.Range of f(x)=cot−1x+tan−1x+cosec−1x is2.[π2,3π2]C.Range of f(x)=cot−1x+tan−1x+cos−1x is3.{0,π}D.Range of f(x)=sec−1x+ cosec−1x+sin−1x is4.(π2,3π2)

A
A- 1, B- 4, C- 2, D- 3
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B
A- 4, B- 1, C- 3, D- 2
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C
A- 4, B- 2, C- 1, D- 3
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D
A- 4, B- 1, C- 2, D- 3
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Solution

## The correct option is C A- 4, B- 1, C- 2, D- 3A) f(x)=sin−1x+cos−1x+cot−1x=π2+cot−1xcot−1xϵ(0,π)⇒f(x)ϵ(π2,3π2)B) f(x)=cot−1x+tan−1x+csc−1x=π2+csc−1xAs csc−1xϵ[−π2,0)∪(0π2]⇒f(x)ϵ[0,π2)∪(π2,π]C) f(x)=cot−1x+tan−1x+cos−1x=π2+cos−1xAs cos−1xϵ[0,π]⇒f(x)=[π2,3π2]D) f(x)=sec−1x+csc−1x+sin−1xAs sec−1xϵ[0,π2)∪(π2,π], csc−1xϵ[−π2,0)∪(0π2] and sin−1xϵ[−π2,π2]⇒f(x)ϵ{0,π}

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