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If solution of `cot(sin^(-1)sqrt(1-x^(2)))=sin(tan^(-1)(xsqrt(6))),x!=0` is `1/psqrt(q/r)` where `p,q,r` are prime then value of `(p+q-r)/p` is |
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Answer» Correct Answer - 2 `cot(sin^(-1)sqrt(1-x^(2)))` `x/(sqrt(1-x^(2))` `sin(tan^(-1)xsqrt(6))=(xsqrt(6))/(sqrt(6x^(2)+1))` `implies(sqrt(6))/(sqrt(6x^(2)+1))=1/(sqrt(1-x^(2)))implies12x^(2)=5` `impliesx=+-1/2sqrt(5/3)` so `x=1/2sqrt(5/3)` (but `x` will be positive `impliesp=2, q=5, r=3` So `(p+q-r)/p=(2+5-3)/2=2` |
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