Multiple choice

Choose the correct answer from the alternatives given : What is the value of $sin^3 60^\circ \, cot 30^\circ \, - \, 2 sec^2 45^\circ \, + 3 cos 60^\circ \, tan 45^\circ \, - tan^2 60^\circ$

  1. $\dfrac{35}8$
  2. $\dfrac{-35}8$
  3. $\dfrac{-11}8$
  4. $\dfrac{11}8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Substitute the values: (sqrt(3)/2)^3 * sqrt(3) - 2*(sqrt(2))^2 + 3*(1/2)*1 - (sqrt(3))^2. This simplifies to (3*sqrt(3)/8)*sqrt(3) - 4 + 1.5 - 3 = (9/8) - 4 + 1.5 - 3 = 1.125 - 5.5 = -4.375, which is -35/8.

AI explanation

Substitute the standard trigonometric values into the given expression to get sin cubed 60 degrees multiplied by cot 30 degrees minus 2 sec squared 45 degrees plus 3 cos 60 degrees multiplied by tan 45 degrees minus tan squared 60 degrees. Evaluating the terms gives (the square root of 3 divided by 2) cubed multiplied by the square root of 3, minus 2 multiplied by the square root of 2 squared, plus 3 multiplied by one half multiplied by 1, minus the square root of 3 squared. This simplifies to 9 divided by 8 minus 4 plus 3 divided by 2 minus 3. Combining the terms by finding a common denominator of 8 yields 9 minus 32 plus 12 minus 24. The final evaluated result is negative 35 divided by 8.

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