Question

1) Cot(4x+pi/4)+3=0

2) tan(1+2x)=2/3

Answer 1

1: \(\cot\left(4x+\frac{\pi}{4}\right)+3=0\)

=>\(\cot\left(4x+\frac{\pi}{4}\right)=-3\)

=>\(4x+\frac{\pi}{4}=arc\cot\left(-3\right)+k\pi\)

=>\(4x=-\frac{\pi}{4}+arc\cot\left(-3\right)+k\pi\)

=>\(x=-\frac{\pi}{16}+\frac14\cdot arc\cot\left(-3\right)+\frac{k\pi}{4}\)

2: \(\tan\left(2x+1\right)=\frac23\)

=>\(2x+1=\arctan\left(\frac23\right)+k\pi\)

=>\(2x=-1+\arctan\left(\frac23\right)+k\pi\)

=>\(x=-\frac12+\frac12\cdot\arctan\left(\frac23\right)+\frac{k\pi}{2}\)