Question

solve for x 2sin^2x-2 cos x =1/2​

Answer 1

Answer:

• The value of x is 60°.

Step-by-step explanation:

Given that:

• 2 sin²x - 2 cos x = 1/2

To Find:

• The value of x.

Finding the value of x:

⟶ 2 sin²x - 2 cos x = 1/2

Taking 2 common in L.H.S.

⟶ 2(sin²x - cos x) = 1/2

⟶ sin²x - cos x = 1/(2 × 2)

⟶ sin²x - cos x = 1/4

⟶ sin²x - cos x = 3/4 - 2/4

⟶ sin²x - cos x = (√3/2)² - 1/2

∵ √3/2 = sin 60° And ∵ 1/2 = cos 60°

⟶ sin²x - cos x = sin²60° - cos 60°

Now we can say that,

⟶ x = 60°

∴ The value of x = 60°

Answer 2

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The value of x is 60°.

Given that:

2 sin²x - 2 cos x = 1/2

To Find:

The value of x.

Finding the value of x:

⟶ 2 sin²x - 2 cos x = 1/2

Taking 2 common in L.H.S.

⟶ 2(sin²x - cos x) = 1/2

⟶ sin²x - cos x = 1/(2 × 2)

⟶ sin²x - cos x = 1/4

⟶ sin²x - cos x = 3/4 - 2/4

⟶ sin²x - cos x = (√3/2)² - 1/2

∵ √3/2 = sin 60° And ∵ 1/2 = cos 60°

⟶ sin²x - cos x = sin²60° - cos 60°

Now we can say that,

⟶ x = 60°