Question

Find the value of x in the following
2sin3x= √3​

Answer 1

Answer:

20°

Step-by-step explanation:

Given a trignometric equation such that,

$2 \sin(3x) = \sqrt{3}$

To solve for x.

Further solving, we get,

$= > \frac{2 \sin(3x) }{2} = \frac{ \sqrt{3} }{2}$

Therefore, we will get,

$= > \sin(3x) = \frac{ \sqrt{3} }{2}$

But, we know that,

• $\sin(60) = \frac{ \sqrt{3} }{2}$

Therefore, we will get,

$= > \sin(3x) = \sin(60)$

Now, both function are same.

Therefore, angles will also be same.

Therefore, we will get,

=> 3x = 60

=> x = 60/3

=> x = 20°

Hence, the value of x is 20°.

Answer 2

GIVEN:

• 2sin3x = √3

TO FIND:

• x

SOLUTION:

2sin3x = √3

On dividing both sides with 2

2sin3x/2 = √3/2

→ sin3x = √3/2

We know that

sin60° = √3/2

Now, substituting sin60° instead of √3/2

→ sin3x = sin60°

→ 3x = 60°

→ x = 60°/3

→ x = 20°

Hence, x = 20°

VERIFICATION:

Taking LHS

Substituting x = 20° in 2sin3x = √3

→ 2sin[3(20°)]

→ 2sin60°

→ 2(√3/2)

→ √3

Now comparing with RHS

√3 = √3

LHS = RHS

Hence , verified!