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Statement-1: tan{cos^(-1)((1)/sqrt(82)...

Statement-1:
`tan{cos^(-1)((1)/sqrt(82))-sin^(-1)((5)/sqrt(26))}=29/3`
Statement-2: `[x cos(cot^(-1))^(2)=51/50rarr x -(1)/5sqrt(2)`

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

we have tan `{cos^(-1)(1)sqrt(82)-sin^(-1)(5)/sqrt(26)}`
`=tan (tan^(-1)9-tan^(-1)5)=tan{tan^(-1)(9-5)/(1+9xx5)}`
`=tan(tan^(-1)2/23)=2/23`
so statement 1 is not true
`rarr (x^(2))/sqrt(x^(2)+1)+(1)sqrt(x^(2)+1)^(2)=51/50 rarr x^(2)+1=51/50 rarr x=(1)/(5sqrt(2))`
so statement 2 is true
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