Sec 330° + cot 480° ?

To find the value of sec 330° + cot 480°, we first need to determine the values of sec 330° and cot 480°.

Secant is the reciprocal of cosine, so sec 330° = 1/cos 330°.

Cos 330° = cos(360° - 30°) = cos 30° = √3/2.

Therefore, sec 330° = 1/(√3/2) = 2/√3 = 2√3/3.

Cotangent is the reciprocal of tangent, so cot 480° = 1/tan 480°.

Tan 480° = tan(480° - 360°) = tan 120° = -√3.

Therefore, cot 480° = 1/(-√3) = -√3/3.

Now, we can find the sum of sec 330° and cot 480°:

sec 330° + cot 480° = 2√3/3 - √3/3 = (2√3 - √3)/3 = √3/3.

Therefore, sec 330° + cot 480° = √3/3.

√3÷3