If the sin 30° = 1 over 2, then the cos 60° = _____.

Solution:

Given, sin 30° = 1 over 2

We have to find cos 60°

Using double angle formula,

cos(2θ) = cos²θ - sin²θ

Using trigonometric identity,

sin²θ + cos²θ = 1

So, cos²θ = 1 - sin²θ

Now, cos(2θ) = 1 - sin²θ - sin²θ

cos(2θ) = 1 - 2 sin²θ

Given, sin 30° = 1/2

Now, cos 2(30°) = 1 - 2 sin²30°

cos 60° = 1 - 2(1/2)²

= 1 - 2(1/4)

= 1 - 2/4

= 1 - 1/2

= 1/2

Therefore, cos 60° = 1/2

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If the sin 30° = 1 over 2, then the cos 60° = _____.

Summary:

If the sin 30° = 1 over 2, then the cos 60° = 1/2.