Statement : $$1)$$ Cosece−$$112+12$$>Sec−$$112+12Statement$$ : $$2)Cosec$$−$$1x$$

Correct option is 31 is true but 2 is false.

Questions

Statement : 1) $C o \sec e^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}}) > S e c^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}})$
Statement : 2) $C o \sec^{- 1} x < S e c^{- 1} x$ if $1 \leq x < \sqrt{2}$

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Both 1,2 are true , and 2 is the correct explanation of 1.

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detailed solution

Correct option is C

If Cosec-1x>Sec-1x⇒Cosec-1x>π2-Cosec-1x⇒Cosec-1x>π4⇒1≤x<2 and 12+12∈[1,2]∴Statement 1 is true and statement 2 is false.

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Statement : 1) Cosece−112+12>Sec−112+12Statement : 2)Cosec−1x<Sec−1x if1≤x<2

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Statement : 1) $C o \sec e^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}}) > S e c^{- 1} (\frac{1}{2} + \frac{1}{\sqrt{2}})$
Statement : 2) $C o \sec^{- 1} x < S e c^{- 1} x$ if $1 \leq x < \sqrt{2}$