What is the general solution for 2cos(x)=sec(x) ?

The general solution for 2cos(x)=sec(x) is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin

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2cos(x)=sec(x)

2 cos (x) = sec (x)

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solution steps

2 cos (x) = sec (x)

Subtract

sec (x)

from both sides

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

Rewrite using trig identities

\frac{2}{sec ( x )} - sec (x) = 0

Solve by substitution

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

sec (x) = 2 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

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

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

tan (5 x) = - 1

x, 7 y^{2} + sin (3 x) = 12 - y^{4}

sin (\frac{π x}{2}) + 1 = 0

sin (x + 6 0^{\circ}) = - 0.4

1 = sin (2 x)

What is the general solution for 2cos(x)=sec(x) ?
The general solution for 2cos(x)=sec(x) is x= pi/4+2pin,x=(7pi)/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin