The value of (1 + sec 20° + cot 70°) * (1 - cosec 20° + tan 70°) is ?

cot 70° = cot (90° - 20°) = tan 20°
tan 70° = tan (90° - 20°) = cot 20°
$$(1 + sec 20^{\circ} + cot 70^{\circ}) = (1 + sec 20^{\circ} + tan 20^{\circ}) $$ $$=\frac{cos 20^{\circ} + sin 20^{\circ} + 1}{cos20^{\circ}}$$

$$(1 + cosec 20^{\circ} + tan70^{\circ}) = (1 - cosec 20^{\circ} + cot20^{\circ}) $$ $$ = \frac{cos 20^{\circ} + sin 20^{\circ} - 1}{sin20^{\circ}}$$

$$(1 + sec 20^{\circ} + cot 70^{\circ}) \times (1 - cosec 20^{\circ} + tan 70^{\circ}) $$ $$=\frac{cos 20^{\circ} + sin 20^{\circ} + 1}{cos20^{\circ}} \times \frac{cos 20^{\circ} + sin 20^{\circ} - 1}{sin20^{\circ}}$$

$$= \frac{(cos 20^{\circ} + sin 20^{\circ})^2 - 1}{sin 20^{\circ}cos20^{\circ}}$$

$$= \frac{cos^2 20^{\circ} + sin^2 20^{\circ} + 2sin 20^{\circ}cos20^{\circ} - 1}{sin 20^{\circ}cos20^{\circ}}$$

$$=\frac{ 2sin 20^{\circ}cos20^{\circ} }{sin 20^{\circ}cos20^{\circ}} =2$$

Hence Option C is the correct answer.