Question

X 4.4.55 Find all real numbers in the interval [0, 21) that satisfy the equation. Use radian measure. 14 sin ?x-2 sin x = cos²x The solution set is (Round to the nearest tenth as needed. Use a comma to separate answers as needed.)

Answer 1

The solution is given below

The given equation is 1 Sin 2x-2Cr2=Cs-1 D And we know that cos2x = -sinn So, 148inek -25inx =l-Sin2x 14 Sib2x+sin2x – 2sinx-130 15 sinare -2sink-1=0 15 sinza -5sinatzsina-1=0 > 5sink (sina-1)+1(3 sinx-1)=0 ssinat) (3sinxt=0 Sink=-1 or sinx=1 5. n = sint(-Y5), x=sint (13) x= sint (-15) thin x=6.08 1827 and a= 3.342950 wt 3 or If

> x=3.3 radian x=6. I radian 3 And i ez Sini X=0.3390369 thin or e=2.801755 0.3 radian or x=2.0 radian Thus, the solutions solutions of of @ (0,25). are, The solution set is 0.3,2-8, 3.3,6,1} ie. 20.3, 2.0, 3.3, 6.15 radian.