Find the value of $\cot { { 45 }^{ o } } +\cot { { 30 }^{ o } } +\sin { { 150 }^{ o } } $
- $\cfrac { 3+\sqrt { 3 } }{ 2 } $
- $\cfrac { 3+2\sqrt { 3 } }{ 2 } $
- $\cfrac { 3-\sqrt { 3 } }{ 2 } $
- $\cfrac { 3-2\sqrt { 3 } }{ 2 } $
Reveal answer
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B
Correct answer
Explanation
cot(45) = 1. cot(30) = sqrt(3). sin(150) = sin(180-30) = sin(30) = 1/2. Sum = 1 + sqrt(3) + 0.5 = 1.5 + sqrt(3) = (3 + 2*sqrt(3)) / 2.
AI explanation
Evaluate each trigonometric term individually using standard angle values. The cotangent of 45 degrees is 1, and the cotangent of 30 degrees is the square root of 3. Using the reference angle formula for the second quadrant, the sine of 150 degrees equals the sine of 30 degrees, which is one half. Adding these values together gives 1 plus the square root of 3 plus one half, which simplifies to the fraction 3 plus 2 times the square root of 3, all divided by 2.