Final Answer
$x=\arctan\left(\sqrt[4]{5ec^4-1}\right),\:x=\arctan\left(-\sqrt[4]{5ec^4-1}\right)$
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Step-by-step Solution
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1
Multiply $5$ times $e$
$\tan\left(x\right)^4=5ec^4-1$
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$\tan\left(x\right)^4=5ec^4-1$
Learn how to solve trigonometric equations problems step by step online. Solve the equation tan(x)^4=5*ec^4-1. Multiply 5 times e. Removing the variable's exponent. Cancel exponents 4 and \frac{1}{4}. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term \sqrt[4]{5ec^4-1}. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.
Final Answer
$x=\arctan\left(\sqrt[4]{5ec^4-1}\right),\:x=\arctan\left(-\sqrt[4]{5ec^4-1}\right)$