The solution set of `|sinx| < 1/2` is

Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx , and sinx cosx i.e., R(sinx + cosx, sinx cosx) , or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2) . Thus, to solve an equation of the form R(u,v)=0 , we form a polynomial equation in u and than look for solutions. The solution set of sinx + cosx -2sqrt(2) sin x cosx=0 is completely described by

Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx , and sinx cosx i.e., R(sinx + cosx, sinx cosx) , or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2) . Thus, to solve an equation of the form R(u,v)=0 , we form a polynomial equation in u and than look for solutions. The solution set of sinx + cosx -2sqrt(2) sin x cosx=0 is completely described by

4. The solution set of the inequality sinx 3 cosx 0 is U (en 1) 2 (3n +1) (A) (c) U 6n a, (3n 1) 1) (D) none of these

The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-2)(x+1)x) le 0

The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-2)(x+1)x) le 0

The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-2)(x+1)x) le 0

The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-2)(x+1)x) le 0

Find the solution set of the inequality sinx > 1/2.