What is the general solution for 24tan(2x)sec^2(2x)=0 ?

The general solution for 24tan(2x)sec^2(2x)=0 is x=(pin)/2

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24tan(2x)sec^2(2x)=0

24 tan (2 x) sec^{2} (2 x) = 0

x = \frac{πn}{2}

Degrees

x = 0^{\circ} + 9 0^{\circ} n

Solution steps

24 tan (2 x) sec^{2} (2 x) = 0

Solving each part separately

tan (2 x) = 0 or sec^{2} (2 x) = 0

tan (2 x) = 0 : x = \frac{πn}{2}

tan (2 x) = 0

General solutions for

tan (2 x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 x = 0 + πn

2 x = 0 + πn

Solve

2 x = 0 + πn : x = \frac{πn}{2}

2 x = 0 + πn

0 + πn = πn

2 x = πn

Divide both sides by

2

2 x = πn

Divide both sides by

2

\frac{2 x}{2} = \frac{πn}{2}

Simplify

x = \frac{πn}{2}

x = \frac{πn}{2}

x = \frac{πn}{2}

sec^{2} (2 x) = 0 :

No Solution

sec^{2} (2 x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

sec (2 x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

x = \frac{πn}{2}

2 + 3 cos (θ) = 0

cos (2 θ) = - 2

\frac{tan ( θ )}{cos ( θ )} = 1

sin (θ) = - \frac{24}{25}, π < θ < \frac{3 π}{2}

sin (\frac{2 θ}{3}) = 0

What is the general solution for 24tan(2x)sec^2(2x)=0 ?
The general solution for 24tan(2x)sec^2(2x)=0 is x=(pin)/2