Question

If A + B + C = 270°, then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to ______.

Options

• 0

• 1

• 2

• 3

Answer 1

If A + B + C = 270°, then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to 1.

Explanation:

A + B + C = 270°

`\implies` A = B = C = 90°, then

cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C

= cos 180° + cos 180° + cos 180° + 4 sin 90° sin 90° sin 90°

= – 1 – 1 + 4 . 1 . 1 . 1

= – 3 + 4

= 1