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Choose the correct option and justify your choice : 2tan 30°/1+tan230° = (A) sin 60° (B) cos 60°

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Choose the correct option and justify your choice :

2tan 30°/1+tan230° =

(A) sin 60°

(B) cos 60°

(C) tan 60°

(D) sin 30°

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Correct option: (A) sin 60°

Explanation:

Substitute the of tan 30° in the given equation

tan 30° = 1/√3

2tan 30°/1+tan230° = 2(1/√3)/1+(1/√3)2

= (2/√3)/(1+1/3) = (2/√3)/(4/3)

= 6/4√3 = √3/2

= sin 60°

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