Question

6sin30°×cos30°/cos30°-sin30° ?

Answer 1

$\frac{6sin30*cos30}{cos30-sin30}= \frac{6* \frac{1}{2}* \frac{ \sqrt{3}}{2}}{ \frac{ \sqrt{3}}{2}- \frac{1}{2}}= \frac{ \frac{3 \sqrt{3}}{2}}{ \frac{ \sqrt{3}}{2}}= \frac{3 \sqrt{3}}{2}* \frac{2}{ \sqrt{3}}=3$

Answer 2

To simplify the expression, let's start by evaluating the individual trigonometric functions involved.

sin(30°) = 1/2 cos(30°) = √3/2

Now, we can substitute these values into the expression:

6sin(30°) × cos(30°) / (cos(30°) - sin(30°))

= 6 * (1/2) * (√3/2) / (√3/2 - 1/2)

= 6 * (1/2) * (√3/2) / (√3/2 - 1/2)

= 6 * (√3/4) / (√3/2 - 1/2)

Next, we need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:

= (6 * (√3/4) * (√3/2 + 1/2)) / ((√3/2 - 1/2) * (√3/2 + 1/2))

= (6 * (√3/4) * (√3/2 + 1/2)) / ((3/2 - 1/2))

= (6 * (√3/4) * (√3/2 + 1/2)) / (2/2)

= (6 * (√3/4) * (√3/2 + 1/2)) / 1

= 6 * (√3/4) * (√3/2 + 1/2)

= (6 * √3 * (√3 + 1)) / (4 * 2)

= (6 * √3 * √3 + 6 * √3) / 8

= (6 * 3 + 6 * √3) / 8

= (18 + 6√3) / 8

Therefore, the simplified value of the expression 6sin(30°) × cos(30°) / (cos(30°) - sin(30°)) is (18 + 6√3) / 8.