Answer B is also correct.

$tan A+cot A+1 = \frac{sin A}{cos A}+\frac{cos A}{sin A}+1$

$\frac{sin^{2}A+cos^{2}A+sinAcosA}{sinAcosA} = \frac{1+sinAcosA}{sinAcosA}$

=$\frac{1}{sinAcosA}+1 = secAcosecA+1$

$tan A+cot A+1 = \frac{sin A}{cos A}+\frac{cos A}{sin A}+1$

$\frac{sin^{2}A+cos^{2}A+sinAcosA}{sinAcosA} = \frac{1+sinAcosA}{sinAcosA}$

=$\frac{1}{sinAcosA}+1 = secAcosecA+1$