Evaluate cos 60° × cos 30° + sin 60° × sin30°

We need to evaluate cos
cos 60× cos 30 + sin 60× sin30

Solution

We know that

cos 60= 1/2

cos 30= √3/2

sin 60= √3/2

sin 30=1/2

Substituting all the values in the given equation we get

 

⇒ \(\frac{1}{2}\times \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \times \frac{1}{2}\)

 

⇒ \(\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{4}\)

 

⇒  \(\frac{2\sqrt{3}}{4}\)

 

⇒  \(\frac{\sqrt{3}}{2}\)

Answer

cos 60× cos 30+sin 60× sin30= √3/2

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