Question

Cos 55° cos55° + sin55° sin 55° - ctg 45° вычислить

Answer 1

$\cos(55°) \cos(55°) + \sin(55°) \sin(55°) - \cot(45°) = \\ = \cos {}^{2} (55°) + \sin {}^{2} (55°) - \cot(45°) = \\ = 1 - \cot(45°) = 1 - 1 = 0$

Answer 2

To calculate the expression, let's break it down step by step:

1. Recall the trigonometric identity: cos^2θ + sin^2θ = 1.
2. Cosine of 55 degrees (cos55°) can be expressed as cos^2θ.
3. Sine of 55 degrees (sin55°) can be expressed as sin^2θ.
4. Cotangent of 45 degrees (ctg45°) is the reciprocal of the tangent, which is equal to 1.

Now, let's plug in the values and calculate:

cos55° cos55° + sin55° sin55° - ctg45°

cos^2(55°) + sin^2(55°) - 1

Now, using the trigonometric identity cos^2θ + sin^2θ = 1:

1 - 1

The result is 0.