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Question

# Assertion :3sin−1(13)+sin−1(35)<2π/3 and tan−1(2√2−1)>π/3 Reason: If 3sin−1x=π/6, then 6x−8x3−1=0

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion3sin−1(13)+sin−1(35)=sin−1(3×13−4(1/3)3)+sin−1(35)=sin−1(1−427)+sin−1(35)=sin−12327+sin−135<sin−1√32+sin−1√32[∵2327=0.85,35=0.6 and √32=0.86]=π3+π3=2π3and tan−1(2√2−1)>tan−1√3=π3 [∵2√2−1=1.8,√3=1.7]so statement-1 is trueIn statement-2, 33sin−1x=π6⇒sin(3sin−1x)=12⇒3x−4x3=1/2⇒6x−8x3−1=0Showing that statement-2 is also true but does not lead to statemen-1.

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