What is the general solution for sin(x)sec(x)=2sin(x),0<= x<= 2pi ?

The general solution for sin(x)sec(x)=2sin(x),0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/3 ,x=(5pi)/3

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sin(x)sec(x)=2sin(x),0<= x<= 2pi

sin (x) sec (x) = 2 sin (x), 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

Solution steps

sin (x) sec (x) = 2 sin (x), 0 \leq x \leq 2 π

Subtract

2 sin (x)

from both sides

sin (x) sec (x) - 2 sin (x) = 0

Factor

sin (x) sec (x) - 2 sin (x) : sin (x) (sec (x) - 2)

sin (x) (sec (x) - 2) = 0

Solving each part separately

sin (x) = 0 or sec (x) - 2 = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

sec (x) - 2 = 0, 0 \leq x \leq 2 π : x = \frac{π}{3}, x = \frac{5 π}{3}

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

3 cos^{2} (y) - 1 = cos (y) + cos^{2} (y), π \leq y \leq 2 π

sec^{2} (x) + tan (x) = 1, 0 \leq x \leq 2 π

6 tanh^{2} (x) + 5 sech (x) - 7 = 0

2 sin (x) + 2 = 0, 0 \leq x \leq 2 π

2 cos^{2} (x) + 3 cos (x) = 2, 0 \leq x \leq 2 π

What is the general solution for sin(x)sec(x)=2sin(x),0<= x<= 2pi ?
The general solution for sin(x)sec(x)=2sin(x),0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/3 ,x=(5pi)/3