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Question

# Assertion :Statement 1 Range of f(x)=tan−1x+sin−1x+cos−1x is (0,π) Reason: Statement 2 f(x)=tan−1x+sin−1x+cos−1x=π2+tan−1x for xϵ(−1,1]

A
Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
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B
Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
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C
STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
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D
STATEMENT 1 is FALSE and STATEMENT 2 is TRUE
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Solution

## The correct option is D STATEMENT 1 is FALSE and STATEMENT 2 is TRUEFor f(x)=tan−1(x)+sin−1(x)+cos−1(x)The domain is [−1,1]In this domain we can re-write the expression asf(x)=π2+tan−1(x)f(−1)=π2−π4=π4f(1)=π2+π4=3π4Therefore range of f(x) is [π4,3π4]

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