What is the general solution for (sin(x))^{sin(x)}=2 ?

The general solution for (sin(x))^{sin(x)}=2 is No Solution for x\in\mathbb{R}

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

(sin (x))^{s i n (x)} = 2

No Solution for x \in R

Solution steps

(sin (x))^{s i n (x)} = 2

Solve by substitution

sin (x) = \frac{ln ( 2 )}{W _{0} ( ln ( 2 ) )}

sin (x) = \frac{ln ( 2 )}{W _{0} ( ln ( 2 ) )} :

No Solution

Combine all the solutions

No Solution for x \in R

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

sin^{2} (x) - 2 cos (x) - 2 = 0

\frac{1}{2} tan^{2} (x) = 1 - sec (x)

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

2 sec^{2} (x) + 3 (\frac{1}{cos ( x )}) = 2

What is the general solution for (sin(x))^{sin(x)}=2 ?
The general solution for (sin(x))^{sin(x)}=2 is No Solution for x\in\mathbb{R}