Solve the trigonometric equation $\sin\left(6x\right)+\cos\left(6x\right)=1-34\sin\left(22x\right)$

$\tan\left(2x\right)=1$

$2\cos\left(x\right)+\sqrt{3}=0$

$\csc\left(2x\right)-2=0$

$\tan\left(x\right)=\frac{15}{30}$

$\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cdot\cos\left(x\right)$

$\ln\left(\frac{1}{x}\right)+\ln\left(2x^3\right)=\ln\left(486\right)-\ln\left(3\right)$

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}=\sec\left(x\right)$