Question

tan $9^{\circ }$ - tan ${27}^{\circ }$ - tan ${63}^{\circ }$ + tan ${81}^{\circ }$ =

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D

4

tan $9^{\circ }$ - tan ${27}^{\circ }$ - tan ${63}^{\circ }$ + tan ${81}^{\circ }$

= tan $9^{\circ }$ + cot $9^{\circ }$ – (tan ${27}^{\circ }$ + cot ${27}^{\circ }$)

= $\frac{1}{sin{9}^{\circ }.cos{9}^{\circ }}–\frac{1}{sin{27}^{\circ }.cos{27}^{\circ }}$

= $\frac{2[sin{54}^{\circ }–sin{18}^{\circ }]}{sin{18}^{\circ }.sin{54}^{\circ }}$ = 4