Choose the correct option and justify your choice :

Question :

(i)  \(2 tan 30\over 1 + tan^2 30\) =

(a) sin 60

(b) cos 60

(c) tan 60

(d) sin 30

(ii)  \(1 – tan^2 45\over 1 + tan^2 45\) =

(a) tan 90

(b) 1

(c) sin 45

(d) 0

(iii)  sin 2A = 2 sin A is the true when A =

(a) 0

(b) 30

(c) 45

(d) 60

(iv)  \(2 tan 30\over 1 – tan^2 30\) =

(a) cos 60

(b) sin 60

(c) tan 60

(d) sin 30

Solution :

(i)  (a) Because \(2 tan A\over 1 + tan^2 A\) = sin 2A = sin 60

(ii) (d)  Because \(1 – tan^2 45\over 1 + tan^2 45\) = \(1 – 1\over 1 + 1\) = 0

(iii)  (a) Because when A = 0, sin 2A = sin 0 = 0

and, 2 sin A = 2 sin 0 = 2(0) = 0

or sin 2A = 2 sin A, when A = 0

(iv) (c) Because \(2 tan A\over 1 – tan^2 A\) = tan 2A = tan 60

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