01HardQ4303The number of integral solutions xxx of log(x+72)(x−72x−3)2≥0\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0log(x+27)(2x−3x−7)2≥0 is :A8B7C5D6Check answerSkip
02MediumQ4304If the solution of the equation logcosxcotx+4logsinxtanx=1,x∈(0,π2)\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)logcosxcotx+4logsinxtanx=1,x∈(0,2π), is sin−1(α+β2)\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)sin−1(2α+β), where α\alphaα, β\betaβ are integers, then α+β\alpha+\betaα+β is equal to :