Which of the following expressions is equivalent to 3 sin² α - 3 sin⁴ α? A)3 cos⁴ α + cos² α B)-cos² α - 3 cos⁴ α) C)3 (cos² α + cos⁴ α) D)3 (cos² α - cos⁴ α) E)-3 (cos² α - cos⁴ α)

Question

Quizplus · Accepted Answer

We can use the trigonometric identity sin(A-B) = sinAcosB - cosAsinB to rewrite the expression as:
3(sin(α-1/2π) - sin(α-1/4π))
= 3(cos1/4πsinα - cos1/2πsinα)
= 3(cos1/4π + cos1/2π)sinα - the distributive property
Therefore, the equivalent expression is 3(cos1/4π + cos1/2π)sinα, which matches choice D.

Which of the Following Expressions Is Equivalent to 3 Sin2

Which of the Following Expressions Is Equivalent to 3 Sin²