What is cos20∘+cos100∘+cos140∘ equal to ?231/20

The given expression is cos20° + cos100° + cos140°.

We know that cos(180° - θ) = -cosθ and cos(θ) = cos(180° - θ).

So, we can rewrite the expression as follows:

cos20° + cos(180° - 80°) + cos(180° - 40°)

This simplifies to:

cos20° + cos80° - cos40°

We also know that cos(θ + φ) + cos(θ - φ) = 2cosθcosφ.

So, we can rewrite the expression again as follows:

2cos60°cos20° - cos40°

This simplifies to:

2 * (1/2) * cos20° - cos40°

Which simplifies to:

cos20° - cos40°

So, cos20° + cos100° + cos140° = cos20° - cos40°.

Without a calculator, it's hard to simplify this further. But you can use a calculator to find the numerical values of cos20° and cos40°, and then subtract to find the final answer.