Cos10°- 2cos50°- cos70°

Предыдущий
вопрос Следующий
вопрос

First, let's express the given trigonometric values in terms of sine functions using the identity cos(x) = sin(90° - x):

cos(10°) = sin(80°)
cos(50°) = sin(40°)
cos(70°) = sin(20°)

Now, we can rewrite the expression using these sine functions:

sin(80°) - 2sin(40°) - sin(20°)

Next, let's simplify this expression:

sin(80°) - 2sin(40°) - sin(20°)
= 2sin(40°)cos(40°) - 2sin(40°) - sin(20°)
= 2sin(40°)(cos(40°) - 1) - sin(20°)
= 2sin(40°)(2cos²(20°) - 1) - sin(20°)
= 2sin(40°)(2(1 - 2sin²(20°)) - 1) - sin(20°)
= 4sin(40°) - 8sin(40°)sin²(20°) - sin(20°)

Therefore,
cos(10°) - 2cos(50°) - cos(70°)
= 4sin(40°) - 8sin(40°)sin²(20°) - sin(20°)