1.

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)

Answer»

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

Solution :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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