Final answer:
Use the trigonometric identities to find the exact value of sin 170° cos 55° cos +170° sin 55° is √3/2. Hence, option (b) is correct.
Step-by-step explanation:
To find the exact value of sun 170° cos 55° cos +170° sin 55°, we can use the trigonometric identities. By using the double-angle formula for sine and cosine, we can rewrite the expression as:
sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) - sin²(θ).
Substituting the values, we have:
sin(170°)cos(55°) + cos(170°)sin(55°) = 2sin(170° + 55°)cos(170° - 55°) = 2sin(225°)cos(115°).
Using the reference angles, sin(225°) = -sin(45°) = -1/√2 and cos(115°) = -cos(65°) = -cos(90° - 65°) = -sin(65°) = -√3/2.
Substituting these values back into the expression:
2(-1/√2)(-√3/2) = √2/2 * √3/2 = √6/4 = √3/2.
Therefore, the exact value of sin 170° cos 55° cos +170° sin 55° is √3/2 (option b).