Question

2sin210°+6cos450°+tg240°+ctg120°

Answer 1

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Answer 2

To evaluate the trigonometric expression, we need to first find the trigonometric values for the given angles and then substitute them into the expression.

1. sin(210°) = sin(180° + 30°) = -sin(30°) = -1/2
2. cos(450°) = cos(360° + 90°) = cos(90°) = 0 (cosine of 90° is 0)
3. tan(240°) = tan(180° + 60°) = tan(60°) = √3 (square root of 3)
4. cot(120°) = 1 / tan(120°) = 1 / √3 = √3 / 3

Now, let's substitute these values back into the original expression:

2sin(210°) + 6cos(450°) + tan(240°) + cot(120°) = 2*(-1/2) + 6*0 + √3 + √3/3 = -1 + √3 + √3/3

To combine the square root terms, we can write the expression as:

= -1 + (3√3 + √3) / 3 = -1 + 4√3 / 3

So, the final value of the expression is -1 + 4√3 / 3.