Question

Cos11*cos21+cos69*cos79-cos10=

Answer 1

Воспользуемся формулой приведения cos (П/2-а)= cos (90-а)= sin а и формулой сложения cos(x-y)=cos x*cosy+sinx*siny:

cos11*cos21+cos69*cos79-cos10= cos11*cos21+ cos(90-21)*cos(90-11)-cos 10=

=  cos11*cos21+sin21*sin 11-cos10= cos(21-11)-cos10=cos10-cos10=0

 

  

 

 

 

 

 

Answer 2

To evaluate the expression cos(11) * cos(21) + cos(69) * cos(79) - cos(10), we can use the trigonometric identities and a scientific calculator to obtain the numerical result.

Let's break it down step by step:

1. Convert the angles from degrees to radians: cos(11°) = cos(11 * π / 180) ≈ 0.9816 cos(21°) = cos(21 * π / 180) ≈ 0.9272 cos(69°) = cos(69 * π / 180) ≈ 0.3420 cos(79°) = cos(79 * π / 180) ≈ 0.1450 cos(10°) = cos(10 * π / 180) ≈ 0.9848

2. Substitute the values back into the expression: 0.9816 * 0.9272 + 0.3420 * 0.1450 - 0.9848

3. Evaluate the expression using a calculator or mathematical software: 0.9096 + 0.04959 - 0.9848 ≈ -0.02561

Therefore, cos(11) * cos(21) + cos(69) * cos(79) - cos(10) ≈ -0.02561.