`cos 2x + a sin x = 2a - 7` has a solution if

Let S be the set of all alpha in R such that the equation, cos 2x + alpha sin x = 2alpha -7 has a solution. The S, is equal to

Prove that the equation cos 2x + a sin x = 2a - 7 possesses a solution if 2 le a le 6 .

Let the set of all a in R such that the equation cos2x+a sin x=2a-7 has a solution be [p,q] and r=tan9^(@)-tan27^(@)-(1)/(cot63^(@))+tan81^(@) ,then pqr is equal to

If the equation cos2x+alpha sin x=2 alpha-7 has a solution.Then range of alpha is

The equation a "cos" x - "cos" 2x = 2a-7 passesses a solution if