What is the general solution for sec(4θ)-2=0 ?

The general solution for sec(4θ)-2=0 is θ= pi/(12)+(pin)/2 ,θ=(5pi}{12}+\frac{pin)/2

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sec(4θ)-2=0

sec (4 θ) - 2 = 0

θ = \frac{π}{12} + \frac{πn}{2}, θ = \frac{5 π}{12} + \frac{πn}{2}

Solution steps

sec (4 θ) - 2 = 0

Move

2

to the right side

sec (4 θ) = 2

General solutions for

sec (4 θ) = 2

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

Solve

4 θ = \frac{π}{3} + 2 πn : θ = \frac{π}{12} + \frac{πn}{2}

Solve

4 θ = \frac{5 π}{3} + 2 πn : θ = \frac{5 π}{12} + \frac{πn}{2}

θ = \frac{π}{12} + \frac{πn}{2}, θ = \frac{5 π}{12} + \frac{πn}{2}

3 sin (θ) = 1 + cos (θ)

cos (θ) = \frac{6}{10}

cos (x) \cdot tan (x) - cos (x) = 0

tan (θ) = 653

- 5 sin^{2} (x) - 4 cos (x) = - 4

What is the general solution for sec(4θ)-2=0 ?
The general solution for sec(4θ)-2=0 is θ= pi/(12)+(pin)/2 ,θ=(5pi}{12}+\frac{pin)/2