What is the general solution for cos(θ)+2sec(θ)=-3 ?

The general solution for cos(θ)+2sec(θ)=-3 is θ=pi+2pin

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cos(θ)+2sec(θ)=-3

cos (θ) + 2 sec (θ) = - 3

θ = π + 2 πn

Solution steps

cos (θ) + 2 sec (θ) = - 3

Subtract

- 3

from both sides

cos (θ) + 2 sec (θ) + 3 = 0

Rewrite using trig identities

3 + \frac{1}{sec ( θ )} + 2 sec (θ) = 0

Solve by substitution

sec (θ) = - \frac{1}{2}, sec (θ) = - 1

sec (θ) = - \frac{1}{2} :

No Solution

sec (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = π + 2 πn

3 tan^{2} (θ) + 7 tan (θ) - 2 = 4

4 sin^{2} (x) = 0

5 cos (2 θ) = - 5 cos (θ)

sin (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

cos (4 x) cos (x) + sin (4 x) sin (x) = \frac{1}{2}

What is the general solution for cos(θ)+2sec(θ)=-3 ?
The general solution for cos(θ)+2sec(θ)=-3 is θ=pi+2pin