Question

Heyy !

Can anyone Help Me with this ?​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given :-

2 Cos θ -√3 = 0

To find :-

Find the following :

1) The value of θ

2) Prove that Sin (2θ) = 2 Sin θ Cos θ

Solution :-

Finding the value of θ:-

Given that

2 Cos θ - √3 = 0

=> 2 Cos θ = √3

=> Cos θ = √3/2

=> Cos θ = Cos 30°

=> θ = 30°

The value of θ = 30°

Proving Sin 2θ = 2 Sin θ Cos θ:-

Now,

On taking LHS

=> Sin 2θ

=> Sin 2(30°)

=> Sin 60°

=> √3/2 ------(1)

On taking RHS

=> 2 Sin θ Cos θ

=> 2 Sin 30° Cos 30°

=> 2(1/2)(√3/2)

=> √3/2 --------(2)

From (1) &(2)

LHS = RHS

Sin 2θ = 2 Sin θ Cos θ

Hence, Proved.

Answer:-

1) The value of θ is 30°

2) Sin 2θ = 2 Sin θ Cos θ

Used formulae:-

→ Sin 30° = 1/2

→ Cos 30° = √3/2

→ Sin 60° = √3/2