Multiple choice

The value of $\displaystyle \sin 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+$ $cosec 60^{\circ}+\cot 90^{\circ}$ is equal to

  1. $\displaystyle \dfrac{5\sqrt{3}-6}{6}$
  2. $\displaystyle \dfrac{-6+7\sqrt{3}}{6}$
  3. $0$
  4. $2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

sin 0 = 0, cos 30 = sqrt(3)/2, tan 45 = 1, cosec 60 = 2/sqrt(3), cot 90 = 0. Sum = 0 + sqrt(3)/2 - 1 + 2/sqrt(3) + 0 = (3/2sqrt(3) + 4/2sqrt(3)) - 1 = 7/2sqrt(3) - 1 = (7sqrt(3)/6) - 1 = (7sqrt(3)-6)/6.

AI explanation

Substitute the standard trigonometric values into the expression to get 0 plus the square root of 3 over 2 minus 1 plus 2 over the square root of 3 plus 0. By rationalizing the third term, the expression becomes the square root of 3 over 2 minus 1 plus 2 times the square root of 3 over 3. Combining these terms over a common denominator of 6 yields negative 6 plus 7 times the square root of 3, all divided by 6.

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