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If `log_(sinx)(cos x) = (1)/(2)`, where `x in (0, (pi)/(2))`, then the value of `sin x` is equal to-A. `(1)/(sqrt(3))`B. `(sqrt(5) - 1)/(2)`C. `(2)/(sqrt(3))`D. `(sqrt(5) + 1)/(2)` |
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Answer» Correct Answer - B `log_(sinx)cosx = (1)/(2) rArr cosx = (sinx)^((1)/(2))` `rArr cos^(2)x = sin x rArr sin^(2)x + sin x - 1 = 0` `rArr sinx = (sqrt(5) - 1)/(2)` as `x in(0,(pi)/(2))` |
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