Choose the correct option and justify your choice : sin 2A = 2 sin A is true when A = ? (A) 0° (B) 30° (C) 45° (D) 60°

Answer: (A) 0°

sin 2A = 2 sin A is true when A = 0°

To find the value of A, substitute the degree given in the options one by one

As

sin 2A = sin 0° = 0

2 sin A

= 2 sin 0°

= 2 × 0

= 0

or,

Apply the sin 2A formula, to find the degree value

sin 2A = 2sin A cos A

⇒2sin A cos A = 2 sin A

⇒ 2cos A = 2

⇒ cos A

= 1

Now, we have to check, to get the solution as 1, which degree value has to be applied.

When 0 degree is applied to cos value, i.e.,

cos 0 =1

Therefore, ⇒ A = 0°

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