Question

The equation $asinx+cos2x+1-a=0$ has a solution if

• A. $a>6$
• B. $a<0$
• C. $a\le 4$
• D. $a=12$

Answer 1

The correct option is A $a>6$

Given equation is $asinx+cos2x+1-a=0$

$\Rightarrow asinx+1-2si{n}^{2}x+1-a=0$

$\Rightarrow 2si{n}^{2}x-asinx+a-2=0$

For the equation to have solution , the determinant should be positive

$\Rightarrow a^2-8a+16\ge 0$

$\Rightarrow a\ge 4$

Therefore for $a>6$ , the given equation has a solution

Therefore option $A$ is correct