Question

Solve. sin2x- cosx=1. 0≤x<2π

a. 0, 5.07
b. 3.14, 4.32
c. 3.14, 4.36
d. 0.42, 1.89, 2.95, 4.21

Please explain your answer.

Answer 1

sin2x - cosx = 1
or, 2*sin x* cos x - cos x=1
or, cos x (2*sin x -1) =1
So, we have
either cos x =1 or (2*sin x-1)= 1
If cos x =1 , then x = 0 degree
If (2*sin x-1) =1, then
2*sin x = 1+1
or, sin x = 1
or, sin x = sin 90
So, x = 90 degree = 3.14/2 radian = 1.57