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

The general solution for sec^2(x)-2=0,0<= x<= 2pi is x= pi/4 ,x=(7pi)/4 ,x=(3pi)/4 ,x=(5pi)/4

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sec^2(x)-2=0,0<= x<= 2pi

sec^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

Solution steps

sec^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

Solve by substitution

sec (x) = 2, sec (x) = - 2

sec (x) = 2, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{7 π}{4}

sec (x) = - 2, 0 \leq x \leq 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

Combine all the solutions

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

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

\frac{1}{2} = sin (2 θ)

1 - 2 sin (θ) = - 1

sin (2 x) + sin (x) = sin (3 x)

sin (2 x) = 23 sin^{2} (x)

What is the general solution for sec^2(x)-2=0,0<= x<= 2pi ?
The general solution for sec^2(x)-2=0,0<= x<= 2pi is x= pi/4 ,x=(7pi)/4 ,x=(3pi)/4 ,x=(5pi)/4