Solve 4sin4 x cos4 x = 1

Evaluate

4 sin (4) \times x cos (4) \times x = 1

Multiply

More Steps

4 sin (4) cos (4) \times x^{2} = 1

Divide both sides

\frac{4 sin ( 4 ) cos ( 4 ) \times x ^{2}}{4 sin ( 4 ) cos ( 4 )} = \frac{1}{4 sin ( 4 ) cos ( 4 )}

Divide the numbers

x^{2} = \frac{1}{4 sin ( 4 ) cos ( 4 )}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{4 sin ( 4 ) cos ( 4 )}

Simplify the expression

x = \pm (- \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )})

Separate the equation into 2 possible cases

x = - \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )} x = - (- \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )})

Solve the equation

x = - \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )} x = \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )}

Solution

x_{1} = - \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )}, x_{2} = \frac{sin ( 4 ) cos ( 4 )}{2 sin ( 4 ) cos ( 4 )}

Alternative Form

x_{1} \approx - 0.7109, x_{2} \approx 0.7109

Solve the quadratic equation