Question

Cos40°cos20°-sin40°sin20°;2)cos70°cos40°+sin70°sin40°​

Answer 1

$\cos(40) \cos(20) - \sin(40) \sin(20) = \cos(40 + 20) = \cos(60)$

$\cos(70) \cos(40) + \sin(70) \sin(40) = \cos(70 - 40) = \cos(30)$

Answer 2

To simplify the expressions, we can use the trigonometric identities:

1. Cosine of the difference of two angles:

cos(A - B) = cosA * cosB + sinA * sinB

2. Cosine of the sum of two angles:

cos(A + B) = cosA * cosB - sinA * sinB

Let's use these identities to simplify the given expressions:

1. cos(40°) * cos(20°) - sin(40°) * sin(20°):

Using the cosine of the difference of two angles identity:

cos(40°) * cos(20°) - sin(40°) * sin(20°) = cos(40° - 20°) = cos(20°)

So, the simplified expression is: cos(20°)

2. cos(70°) * cos(40°) + sin(70°) * sin(40°):

Using the cosine of the sum of two angles identity:

cos(70°) * cos(40°) + sin(70°) * sin(40°) = cos(70° + 40°) = cos(110°)

However, 110° is outside the range of the unit circle, and the cosine function is periodic with a period of 360°. So, we need to find an equivalent angle within the unit circle:

110° - 360° = -250°

Now, we have an angle (-250°) within the unit circle:

cos(-250°) = cos(250°)

So, the simplified expression is: cos(250°)