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

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

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

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

x = πn

Degrees

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

Solution steps

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

Solving each part separately

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

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

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

Combine all the solutions

x = πn

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

8 sin^{2} (x) + 6 sin (x) + 1 = 0

sin (\frac{θ}{2}) = 0

tan (\frac{θ}{2} - \frac{π}{4}) = 1

cos^{2} (x) - 3 cos (x) + 2 = 0

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