What is the general solution for e^{(-pi)/(tan(x))}=0.6 ?

The general solution for e^{(-pi)/(tan(x))}=0.6 is x=1.40960…+pin

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e^{(-pi)/(tan(x))}=0.6

e^{\frac{- π}{t a n ( x )}} = 0.6

x = 1.40960 \dots + πn

Solution steps

e^{\frac{- π}{t a n ( x )}} = 0.6

Apply exponent rules

\frac{- π}{tan ( x )} = ln (0.6)

Solve

\frac{- π}{tan ( x )} = ln (0.6) : tan (x) = - \frac{π}{ln ( 0.6 )}

tan (x) = - \frac{π}{ln ( 0.6 )}

Apply trig inverse properties

x = arctan (- \frac{π}{ln ( 0.6 )}) + πn

Show solutions in decimal form

x = 1.40960 \dots + πn

6 cos (2 x) = - 6 cos (x)

3 sec (2 θ) = 2

2 sin^{2} (x) + 3 sin (x) - 1 = 0

- 6 cos^{2} (θ) + cos (θ) + 7 = 5

y, arccot (x y) = ln (sin (x))

What is the general solution for e^{(-pi)/(tan(x))}=0.6 ?
The general solution for e^{(-pi)/(tan(x))}=0.6 is x=1.40960…+pin