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If `cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))}` then x equalsA. `(b)/sqr(2b^(2)-a^(2))`B. `(a)/sqr(2b^(2)-a^(2))`C. `sqrt(b^(2)-a^(2))/(a)`D. `sqrt(b^(2)-a^(2))/(b)` |
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Answer» We have `cot (cos^(-1)x) = see {tan^(-1)(a)/sqrt(b^(2)-a^(2))}` `rarr cot{cot^(-1)(x)/sqrt(1-x^(2))}=sec { sec^(-1)(b)/sqrt(b^(2)-a^(2))}` `rarr (1-x^(2))/(x^(2))=(b^(2)-a^(2))/(b^(2))` `rarr (1)/(x^(2))-1=1-(a^(2))/(b^(2) rarr (1)/(x^(2))= (2b^(2)-a^(2))/(b^(2)) rarr x= (b)/sqrt(2b^(2)-a^(2))` |
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