Determine all solutions of the trigonometric equation 1-cos2x=4sinx. Solution We\'ll apply the following formula: 1 - cos 2x = 2*[sin (2x/2)]^2 1 - cos 2x = 2*(sin x)^2 (1) We\'ll re-write the equation, replacing the left side by (1): 2*(sin x)^2 = 4*sin x We\'ll divide by 2: (sin x)^2 = 2*sin x We\'ll move all terms to on side: (sin x)^2 - 2*sin x = 0 We\'ll factorize by sin x: (sin x)*(sin x - 2) = 0 We\'ll cancel each factor: sin x = 0 x = (-1)^k*arcsin 0 + k*pi x = k*pi sin x = 2 impossible since the value of sine function cannot be larger than 1. The only possible set of solutionsof the trigonometric equation,, for anyintegerk,is: {k*pi, }..