Question

If sin(α) * cos(α) = 1.2, then what is sin³(α) * cos³(α)?

a) 1.728
b) 0.512
c) 2.0736
d) 0.138

Answer 1

So, the correct answer is:

a) 1.728

Step-by-step explanation:

Answer 2

To solve sin³(α) * cos³(α), we can start by cubing both sides of the equation sin(α) * cos(α) = 1.2. Then, using the identity sin²(α) = 1 - cos²(α), we can rewrite the equation and solve for cos⁵(α). Substituting this value back into the equation, we can find the answer.

Step-by-step explanation:

To find sin³(α) * cos³(α), we can start by cubing both sides of the equation sin(α) * cos(α) = 1.2. This gives us (sin(α) * cos(α))³ = (1.2)³.

Next, we can use the identity sin²(α) = 1 - cos²(α) to rewrite the equation in terms of sin²(α) or cos²(α). We get (1 - cos²(α)) * cos³(α) = (1.2)³.

Expanding and rearranging the equation, we have cos³(α) - cos⁵(α) = (1.2)³. Now we can solve for cos⁵(α) by subtracting cos³(α) from both sides of the equation.

Finally, we can substitute the value of cos⁵(α) back into the equation sin³(α) * cos³(α) = 1.2 to find the answer.