how to Find zeros of tan z and cot z

Question : how to Find zeros of tan z and cot z

Solution :

(a)zeros of tan z

We can write \[tan\ z\ =\frac{\sin{z}}{\cos{z}}\] Now zeros of tan z are the zeros of sin z that is \[\sin{z}=0\] \[\sin{z}=\sin{n\pi},\ n=0,\pm1,\pm2,\pm3,\ldots.. \] Are the required zeros of sin z

(b ) zeros of cot z

We can write \[cot\ z\ =\frac{\cos{z}}{\sin{z}}\] Since zeros of cot z are the zeros of cos z that is \[\cos{z}=0\] \[ \cos{z}=\cos{\frac{n\pi}{2}},\ n=\pm1,\pm3,\pm5\ldots.. \] Are the required zeros of cot z