Choose the correct option and justify your choice :

$$\dfrac{ 2\;tan \;30°}{1+tan^230°}$$ =

(A) sin 60°

(B) cos 60°

(C) tan 60°

(D) sin 30°

Asked by Pragya Singh | 1 year ago |  122

##### Solution :-

Right answer is  (A)  sin 60°

Substitute the of tan 30° in the given equation

tan 30° = $$\dfrac{1}{\sqrt{3}}$$

2$$(\dfrac{1}{\sqrt{3}})=1+(\dfrac{1}{\sqrt{3}})2$$

$$\dfrac{2}{\sqrt{3}}=1+\dfrac{1}{3}$$

$$\dfrac{6\sqrt{3}}{4}=\dfrac{\sqrt{3}}{2}$$ = sin 60°

The obtained solution is equivalent to the trigonometric ratio sin 60°

Answered by Abhisek | 1 year ago

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