Assertion : cosec ^ -1 3 2 + ^ -1 2 3 -2 ^ -1 1 7 - ^ -1 7= ^ -1 7 Reason : sin –1 x +…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Assertion :
\(\operatorname{cosec}^{-1} \frac{3}{2}+\cos ^{-1} \frac{2}{3}\)\(-2 \cot ^{-1} \frac{1}{7}-\cot ^{-1} 7=\cot ^{-1} 7\)
Reason : sin–1 x + cos–1 x = \(\frac{\pi}{2},\) tan–1 x + cot–1 x = \(\frac{\pi}{2},\)
cosec–1 x = sin–1 \(\frac{1}{x},\) and for x > 0, cot–1 x = tan–1 \(\frac{1}{x}\)
\(\operatorname{cosec}^{-1} \frac{3}{2}+\cos ^{-1} \frac{2}{3}\)\(-2 \cot ^{-1} \frac{1}{7}-\cot ^{-1} 7=\cot ^{-1} 7\)
Reason : sin–1 x + cos–1 x = \(\frac{\pi}{2},\) tan–1 x + cot–1 x = \(\frac{\pi}{2},\)
cosec–1 x = sin–1 \(\frac{1}{x},\) and for x > 0, cot–1 x = tan–1 \(\frac{1}{x}\)
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(D) If Assertion is false, Reason is true.
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