Question

Cos 147 *cos 67+sin 147 *sin 67

Answer 1

$sin \alpha cos \beta -cos \alpha sin \beta =sin( \alpha -\beta )\\\\cos147=cos(90+57)=-sin57\\\\sin147=sin(90+57)=cos57\\\\cos147cos67+sin147sin67=-sin57cos47+cos57sin47=\\\\=sin(47-57)=sin(-10)=-sin10$

Answer 2

To solve the expression cos(147) * cos(67) + sin(147) * sin(67), we can use the trigonometric identity for the cosine of the sum of two angles:

cos(A + B) = cos(A) * cos(B) - sin(A) * sin(B)

In this case, A = 147 and B = 67. Plugging in the values, we have:

cos(147) * cos(67) + sin(147) * sin(67) = cos(147 + 67)

Since cos(147 + 67) is equal to cos(214), we can evaluate it to get the final result:

cos(214) ≈ -0.9914

Therefore, cos(147) * cos(67) + sin(147) * sin(67) is approximately equal to -0.9914.