Question

. Choose the correct option and justify your choice : (i) 2tan 30°/1+tan230° = (A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30° (ii) 1-tan245°/1+tan245° = (A) tan 90° (B) 1 (C) sin 45° (D) 0 (iii) sin 2A = 2 sin A is true when A = (A) 0° (B) 30° (C) 45° (D) 60° (iv) 2tan30°/1-tan230° = (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°

Answer 1

SOLUTION

(i) (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°

Answer 2

Answer:

upper Solution is good explanation