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°
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(i) (A) is correct.
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°
The obtained solution is equivalent to the trigonometric ratio sin 60°
(ii) (D) is correct.
Substitute the of tan 45° in the given equation
tan 45° = 1
1-tan245°/1+tan245° = (1-12)/(1+12)
= 0/2 = 0
The solution of the above equation is 0.
(iii) (A) is correct.
To find the value of A, substitute the degree given in the options one by one
sin 2A = 2 sin A is true when A = 0°
As sin 2A = sin 0° = 0
2 sin A = 2 sin 0° = 2 × 0 = 0
(iv) (C) is correct.
Substitute the of tan 30° in the given equation
tan 30° = 1/√3
2tan30°/1-tan230° = 2(1/√3)/1-(1/√3)2
= (2/√3)/(1-1/3) = (2/√3)/(2/3) = √3 = tan 60°
The value of the given equation is equivalent to tan 60°.
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