Question

Complete set of values of ‘a’ for which $asi{n}^{2}x+|cosx|-2a=0$ has alteast one solution belongs to the interval

• A. $[-\frac{1}{2},0)$
• B. $[0,\frac{1}{2}]$
• C. $(0,\frac{1}{2}]$
• D. $(0,\frac{1}{2})$

Answer 1

The correct option is C

$(0,\frac{1}{2}]$

$a-aco{s}^{2}x+|cosx|-2a=0\Rightarrow a=\frac{|cosx|}{1+co{s}^{2}x}=\frac{1}{|cosx|+\frac{1}{|cosx|}}$

$|cosx|\in [0,1]\Rightarrow |cosx|+\frac{1}{|cosx|}\in [2,\infty )$

$\Rightarrow a\in (0,\frac{1}{2}]$