What is the general solution for sin(x)sec(x)=sin(x) ?

The general solution for sin(x)sec(x)=sin(x) is x=2pin,x=pi+2pin

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sin(x)sec(x)=sin(x)

sin (x) sec (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) sec (x) = sin (x)

Subtract

sin (x)

from both sides

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

Factor

sin (x) sec (x) - sin (x) : sin (x) (sec (x) - 1)

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos (x) + 2 = 0

\frac{2 tan ( 3 x )}{1 - tan ^{2} ( 3 x )} = 1

sin (x) = \frac{3}{3}

cos (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

tan (x) tan (2 x) = 1

What is the general solution for sin(x)sec(x)=sin(x) ?
The general solution for sin(x)sec(x)=sin(x) is x=2pin,x=pi+2pin