Question

2sin2theta=root3 find the value of theta for the equation

Answer 1

Answer : 60°

Solution :
__________

Given that :

$2 \sin 2\alpha = \sqrt{3}$

As we know that :

$\sin2 \alpha = 2 \sin\alpha \cos \alpha$

Now,

$4 \sin\alpha \cos \alpha = \sqrt{3} \\ \\ = > \sin\alpha \cos\alpha = \frac{ \sqrt{3} }{4} \\ \\ = > \sin \alpha \cos\alpha = \frac{ \sqrt{3} }{2} \times \frac{1}{2} \\ \\ As \: we \: know \: that :\: sin60° = \frac{ \sqrt{3} }{2} \: and \: \cos60 = \frac{1}{2} \\ \\ = > \sin60 \cos60 = \frac{ \sqrt{3} }{2} \times \frac{1}{2} \\ \\ = > \alpha = 60°$

So the value will be 60°