What is the general solution for (pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0 ?

The general solution for (pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0 is x=4n

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(pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0

\frac{π ^{2}}{8} sec^{2} (\frac{π x}{4}) tan (\frac{π x}{4}) = 0

x = 4 n

Degrees

x = 0^{\circ} + 229.18311 \dots^{\circ} n

Solution steps

\frac{π ^{2}}{8} sec^{2} (\frac{π x}{4}) tan (\frac{π x}{4}) = 0

Solving each part separately

sec^{2} (\frac{π x}{4}) = 0 or tan (\frac{π x}{4}) = 0

sec^{2} (\frac{π x}{4}) = 0 :

No Solution

sec^{2} (\frac{π x}{4}) = 0

Apply rule

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

sec (\frac{π x}{4}) = 0

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

No Solution

tan (\frac{π x}{4}) = 0 : x = 4 n

tan (\frac{π x}{4}) = 0

General solutions for

tan (\frac{π x}{4}) = 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}

\frac{π x}{4} = 0 + πn

\frac{π x}{4} = 0 + πn

Solve

\frac{π x}{4} = 0 + πn : x = 4 n

\frac{π x}{4} = 0 + πn

0 + πn = πn

\frac{π x}{4} = πn

Multiply both sides by

4

\frac{π x}{4} = πn

Multiply both sides by

4

\frac{4 π x}{4} = 4 πn

Simplify

π x = 4 πn

π x = 4 πn

Divide both sides by

π

π x = 4 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 πn}{π}

Simplify

x = 4 n

x = 4 n

x = 4 n

Combine all the solutions

x = 4 n

What is the general solution for (pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0 ?
The general solution for (pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0 is x=4n