Question

Find the value of $2\sin {30^0}\cos {30^0}$
$
  (a){\text{ tan3}}{{\text{0}}^0} \\
  (b){\text{ cos6}}{{\text{0}}^0} \\
  (c){\text{ sin6}}{{\text{0}}^0} \\
  (d){\text{ cot6}}{{\text{0}}^0} \\
$

Answer 1

Hint: In this question we have to find the value of the given expression, simply use the trigonometric identity that is $\sin 2A = 2\sin A\cos A$, to get the answer.

Complete step-by-step answer:
Given expression
$2\sin {30^0}\cos {30^0}$
As we know the basic trigonometric identity which is $\left( {\sin 2A = 2\sin A\cos A} \right)$. So use this identity in the above expression we have,
Where $\left[ {A = {{30}^0}} \right]$
$ \Rightarrow 2\sin {30^0}\cos {30^0} = \sin \left( {2 \times {{30}^0}} \right)$
$ \Rightarrow 2\sin {30^0}\cos {30^0} = \sin {60^0}$
So this is the required answer.
Hence option (C) is correct.

Note: Whenever we face such types of problems the key concept is to have a good understanding of the basic trigonometric identities, few have been mentioned above. In trigonometry it is always advisable to grasp the trigonometric identities and it gets perfect with more practice.