A) 0
B) \[-1\]
C) \[~-2\]
D) 1
Correct Answer: D
Solution :
[d] \[\because y=tan{{1}^{{}^\circ }}.\,tan{{2}^{{}^\circ }}.\text{ }tan{{3}^{{}^\circ }}.\text{ }tan{{4}^{{}^\circ }}.....tan{{89}^{{}^\circ }}\] \[=tan{{1}^{{}^\circ }}.\text{ }tan\left( {{90}^{{}^\circ }}-{{1}^{{}^\circ }} \right).tan{{2}^{{}^\circ }}.\text{ }tan\left( {{90}^{{}^\circ }}-2 \right).....tan{{45}^{{}^\circ }}\]\[=tan{{1}^{{}^\circ }}.\text{ }cot{{1}^{{}^\circ }}.\text{ }tan{{2}^{{}^\circ }}.\text{ }cot{{2}^{{}^\circ }}......\text{ }tan{{.45}^{{}^\circ }}\] \[=1\times 1\times 1..........\times 1=1\]
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