What is the general solution for 4cos(θ)=sec(θ) ?

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

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4cos(θ)=sec(θ)

4 cos (θ) = sec (θ)

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

Solution steps

4 cos (θ) = sec (θ)

Subtract

sec (θ)

from both sides

4 cos (θ) - sec (θ) = 0

Rewrite using trig identities

\frac{4}{sec ( θ )} - sec (θ) = 0

Solve by substitution

sec (θ) = 2, sec (θ) = - 2

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

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

Combine all the solutions

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

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

cot (θ) + 4 csc (θ) = 6

sin (x) 2 = - sin (x)

tan^{3} (x) = 1

sin^{2} (x) - 9 cos (x) - 9 = 0

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