Simplify and find the value: {sin}^(4) a - {cos}^(4) a - 2 {sin}^(2) a ​

Question

Simplify and find the value:

`{sin}^(4) a - {cos}^(4) a - 2 {sin}^(2) a`
​

Answer 1

-1

Explanation:

Trigonometry identity: sin²a + cos²a = 1 ⇔ cos²a = 1 - sin²a

sin⁴a - cos⁴a - 2sin²a

= sin⁴a - (cos²a)² - 2sin²a

= sin⁴a - (1 - sin²a)² - 2sin²a

= sin⁴a - (1 - 2sin²a + sin⁴a) - 2sin²a

= sin⁴a - 1 + 2sin²a - sin⁴a - 2sin²a

= -1