Question

Choose the connect option and
and justify your
choice:
(a) 2tan 30°
1+tan²30°
is equal to.​

Answer 1

(A) is correct. 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° (ii) (D) is correct. 1-tan245°/1+tan245° = (1-12)/(1+12) = 0/2 = 0 (iii) (A) is correct. sin 2A = 2 sin A is true when A = = As sin 2A = sin 0° = 0 2 sin A = 2sin 0° = 2×0 = 0 or, sin 2A = 2sin A cos A ⇒2sin A cos A = 2 sin A ⇒ 2cos A = 2 ⇒ cos A = 1 ⇒ A = 0° (iv) (C) is correct. 2tan30°/1-tan230° = 2(1/√3)/1-(1/√3)2 = (2/√3)/(1-1/3) = (2/√3)/(2/3) = √3 = tan 60°

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