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

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

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

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

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Solving each part separately

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

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (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}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

sec^{2} (x) = 0 :

No Solution

sec^{2} (x) = 0

Apply rule

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

sec (x) = 0

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

No Solution

Combine all the solutions

x = πn

sin (2 θ - \frac{π}{2}) = 1

2 sin^{2} (2 θ) = 1 - sin (2 θ)

cos (θ) = \frac{24}{25}

sec^{2} (x) = 1 - tan^{2} (x)

8 sin^{2} (θ) - 17 sin (θ) + 9 = 0

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