Multiple choice

If $\displaystyle x\cos 60^{\circ}+y\cos 0^{\circ}=3: : : and: : : 4x\sin 30^{\circ}-y\cot 45^{\circ}=2 $, then what is the value of $x$?

  1. $-1$
  2. $0$
  3. $1$
  4. $2$
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D Correct answer
Explanation

Substituting the trigonometric values cos(60) = 1/2, cos(0) = 1, sin(30) = 1/2, and cot(45) = 1 into the given equations yields the system of linear equations: x/2 + y = 3 and 2x - y = 2. Solving this system by substituting y = 2x - 2 into the first equation gives x/2 + 2x - 2 = 3, which simplifies to 5x/2 = 5, resulting in x = 2.

AI explanation

Substituting the standard values cos(60 degrees) = 1/2, cos(0 degrees) = 1, sin(30 degrees) = 1/2, and cot(45 degrees) = 1 into the given equations yields x/2 + y = 3 and 2x minus y = 2. Adding these two equations eliminates y and gives 5x/2 = 5. Solving for x results in x = 2.

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