JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q86

← JEE Main 2021 · 24 Feb · Shift 1

MathematicsInteger+4 / -1Question 86 of 90

The minimum value of α for which the equation $\dfrac4{\sin x}+\dfrac1{1-\sin x}=\alpha$ has at least one solution in $\left(0,\dfrac\pi2\right)$ is _______.

Your answer

Answer and worked solution

Official answer: 9

Minimum of $\frac4s+\frac1{1-s}$ on $(0,1)$ : by Cauchy-Schwarz it is at least $\frac{(2+1)^2}{s+(1-s)}=9$ , reached at $s=\frac23$ .

Answer: 9

Topics:Maxima and minima AM-GM-HM inequalities

← Previous question Next question →

JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 86