What is the value of \( x \) ? \[ \sin (x+34)^{x}=\cos (2 x+20 \] Enter your answer in the box.

Step 1 ：\sin (x+34)^{x}=\cos (2 x+20)

Step 2 ：\sin (x+34)^{x}=\sin(90 - (2 x+20))

Step 3 ：(x+34)^{x}=90-(2x+20)

Step 4 ：\text{The equation has no analytic solutions for } x.