A) 2
B) 3
C) 1
D) 4
Correct Answer: C
Solution :
(c): \[tan{{4}^{{}^\circ }}.\text{ }tan{{43}^{{}^\circ }}.\,tan{{47}^{{}^\circ }}.\,tan{{85}^{{}^\circ }}\] \[=tan{{4}^{{}^\circ }}.\,tan{{43}^{{}^\circ }}.\,tan\left( {{90}^{{}^\circ }}-{{43}^{{}^\circ }} \right).\,tan\left( {{90}^{{}^\circ }}-{{4}^{{}^\circ }} \right)\] \[=tan{{4}^{{}^\circ }}\times tan{{43}^{{}^\circ }}\times cot{{43}^{{}^\circ }}\times cot{{4}^{{}^\circ }}=1\] \[\left[ tan\left( {{90}^{{}^\circ }}-\theta \right)=cot\theta ;\,tan\theta .\,cot\theta -1 \right]\]
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