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

The general solution for sin(x)tan(x)=sin(x),0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(5pi)/4

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

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

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

Solution steps

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

Subtract

sin (x)

from both sides

sin (x) tan (x) - sin (x) = 0

Factor

sin (x) tan (x) - sin (x) : sin (x) (tan (x) - 1)

sin (x) (tan (x) - 1) = 0

Solving each part separately

sin (x) = 0 or tan (x) - 1 = 0

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

tan (x) - 1 = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{5 π}{4}

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

2 tan (x) + sec^{2} (x) = 4

cos (a) + sin (a) = 1

cos (x) = \frac{1}{7}

sin (5 x + 43) = cos (- x + 3 1^{\circ})

sin (x) + 1 = 2 cos^{2} (x)

What is the general solution for sin(x)tan(x)=sin(x),0<= x<= 2pi ?
The general solution for sin(x)tan(x)=sin(x),0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(5pi)/4