Question

prove that sin 780° sin 480° +
COS 240°. COS300 = 1/2​

Answer 1

Answer:

How do you prove that sin 780 × sin 480 + cos 240 × cos 300 =1/2?

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Sin780° = Sin(360 + 360 + 60)° = Sin60° = √3/2.

Sin480° = Sin(360 + 90 + 30)° = Cos30° = √3/2.

Cos240° = Cos(180 + 60)° = -Cos60° = -1/2.

Cos300° = Cos(270 + 30)° = Sin30° = 1/2.

So, Sin780° × Sin480° + Cos240° × Cos300°

= (√3)²/(2)² + (-1)(1)/(2)².

= (3/4) - (1/4).

= (3 - 1)/4.

= 2/4.

= 1/2.

Hence Proved.

Step-by-step explanation:

hopefully this will help you