Question

$
  {\text{If }}x\cos {60^0} - y\cos {0^0} = 3 \\
  4x\sin {360^0} - y\cot {45^0} = 2 \\
 $
Then what is the value of x?
$
  {\text{A}}{\text{. - 1}} \\
  {\text{B}}{\text{. 0}} \\
  {\text{C}}{\text{. 1}} \\
  {\text{D}}{\text{. 2}} \\
 $

Answer 1

Hint: -To solve this type of question you should have knowledge of solving linear equations in two variables. This question is very straightforward: just put the values of trigonometric angles and simple calculation to get an answer.

Complete step-by-step solution -
We have
$
  x\cos {60^0} - y\cos {0^0} = 3 \\
  4x\sin {360^0} - y\cot {45^0} = 2 \\
 $
We know
$
\ cos {60^0} = \dfrac{1}{2},\cos {0^0} = 1 \\
  \sin {360^0} = 0,\cot {45^0} = 1 \\
$
On putting these values our question becomes
$
  \dfrac{x}{2} - y = 3 \\
  0 - y = 2 \\
$
From here we can clearly see y = -2 and on putting y = -2 we get x =2.
Hence option D is the correct option.

Note: -Whenever you get this type of question the key concept of solving is you have to just put the value to get the result. This is a very easy question, just simple calculation and nothing is remaining in the question. You have just remembered values of trigonometric angles.