4cos(θ)-3sec(θ)=0

Solution

4 cos (θ) - 3 sec (θ) = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Solution steps

4 cos (θ) - 3 sec (θ) = 0

Rewrite using trig identities

\frac{4}{sec ( θ )} - 3 sec (θ) = 0

Solve by substitution

sec (θ) = \frac{2 3}{3}, sec (θ) = - \frac{2 3}{3}

sec (θ) = \frac{2 3}{3} : θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sec (θ) = - \frac{2 3}{3} : θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

sin (x) = \frac{π}{6}

(2 sin (4 x) - 1) \cdot (1 + tan (x)) = 0

arctan (θ) = 3

csc (t) = 3735, 0 < t < \frac{π}{2}, cot (t)

- 1 = cos (3 x)