To evaluate this expression, we can use the trigonometric identities:
cos(a+b) = cos(a)cos(b) - sin(a)sin(bsin(a+b) = sin(a)cos(b) + cos(a)sin(b)
Given that the expression is cos(125)cos(5) + sin(55)cos(85), we can rewrite it as:
cos(125+5) + sin(55+85)
Which simplifies to:
cos(130) + sin(140)
Now we can find the values of cosine and sine of 130 and 140 degrees using a calculator:
cos(130) ≈ -0.642sin(140) ≈ 0.6438
Substitute these values back into the expression:
-0.6428 + 0.6438 ≈ 0.001
Therefore, the value of the expression is approximately 0.001.
To evaluate this expression, we can use the trigonometric identities:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
Given that the expression is cos(125)cos(5) + sin(55)cos(85), we can rewrite it as:
cos(125+5) + sin(55+85)
Which simplifies to:
cos(130) + sin(140)
Now we can find the values of cosine and sine of 130 and 140 degrees using a calculator:
cos(130) ≈ -0.642
sin(140) ≈ 0.6438
Substitute these values back into the expression:
-0.6428 + 0.6438 ≈ 0.001
Therefore, the value of the expression is approximately 0.001.