Question

If x + y + z = 180°, then cos 2x + cos 2y – cos 2z is equal to ______.

Options

• 4 sin x . sin y . sin z

• 1 – 4 sin x . sin y . cos z

• 4 sin x . sin y . sin z – 1

• cos A . cos B . cos C

Answer 1

If x + y + z = 180°, then cos 2x + cos 2y – cos 2z is equal to 1 – 4 sin x . sin y . cos z.

Explanation:

cos 2x + cos 2y – cos 2z

= 2 cos(x + y) cos(x – y) – 2 cos² z + 1

= 2 cos(π – z) cos(x – y) – 2 cos² z + 1

= 1 – 2 cos z{cos(x – y) – cos(x + y)}

= 1 – 2 cos z{2 sin x sin y}

= 1 – 4 sin x sin y cos z