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

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

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cos(x)tan(x)-cos(x)=0,0<= x<= 2pi

cos (x) tan (x) - cos (x) = 0, 0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{5 π}{4}

Solution steps

cos (x) tan (x) - cos (x) = 0, 0 \leq x \leq 2 π

Factor

cos (x) tan (x) - cos (x) : cos (x) (tan (x) - 1)

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

Solving each part separately

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

cos (x) = 0, 0 \leq x \leq 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

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

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{π}{4}, x = \frac{5 π}{4}

Since the equation is undefined for:

\frac{π}{2}, \frac{3 π}{2}

x = \frac{π}{4}, x = \frac{5 π}{4}

sin^{2} (2 θ) - 5 sin (2 θ) - 1 = 0

- \frac{π}{30} sin (\frac{π}{90} (x + 20)) = 0

sin (2 x) = - \frac{1}{2}

cos (x) = - \frac{22}{7.28 \cdot 20}

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

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