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The value of `sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)}` isA. `0`B. `(pi)/4`C. `(pi)/6`D. `(pi)/2` |
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Answer» Correct Answer - D `sin^(-1)((sqrt(2-sqrt(3)))/2)=tan^(1)(sqrt((2-sqrt(3))/(2+sqrt(3))))=tan^(-1)(2-sqrt(3))` `(pi)/12` `cos^(-1)((sqrt(12))/4)=cos^(-1)((sqrt3)/2)=(pi)/6` `impliessec^(-1)(sqrt(2))=(pi)/4` `impliessin^(-1)((sqrt(2-sqrt(3)))/2)+cos^(-1)((sqrt(12))/4)+sec^(-1)(sqrt(2))` `=(pi)/12+(pi)/6+(pi)/4+(pi)/2` `implies "cot"(pi)/2=0` and `cos^(-1) (0)=(pi)/2` |
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