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Statement-1: cosec^(-1)(3)/(2)+cos^(-1)...

Statement-1: `cosec^(-1)(3)/(2)+cos^(-1)(2/3)-2cot^(-1)(1/7)-cot^(-1)7=cot^(-1)7` Statement-2: `cos^(-1)x=sin^(-1)((1)/(x)) and for xgt0cot^(-1)x=tan^(-1)((1)/(x))`

A

Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

statement -2 is true (see theory)
using statement -2 we have
`cosec^(-1)3/2+cos^(-1)2/3-2cos^(-1)1/7-cos^(-1)7`
`=(sin^(-1)2/3+cos^(-1)2/3)-cot^(-1)1/7-(tan^(-1)7+cot^(-1)7)`
`=(pi)/(2)-cot^(-1)1/7-(pi)/(2)=-cot^(-1)1/7=-tan^(-1)7`
so statement -1 is not correct
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