Question

Cos^⁴A - Sin^⁴A = 1-2 Sin ²A​

Answer 1

Step-by-step explanation:

To Prove: sin⁴A + cos⁴A = 1 - 2sin²A × cos²A

Solution: sin⁴A + cos⁴A can be expressed as;

α² + β² = (α + β)² - 2αβ

(sin²A)² + (cos²A)² = (sin²A + cos²A)² - 2(sin²A)(cos²A)

$\boxed{\sf sin^{2}\theta + cos^{2}\theta = 1}$

sin

2

θ+cos

2

θ=1

(sin²A)² + (cos²A)² = (1)² - 2(sin²A)(cos²A)

(sin²A)² + (cos²A)² = 1 - 2 × sin²A × cos²A

Hence Proved.

Identities used in the Solution:

α² + β² = (α + β)² - 2αβ

sin²θ + cos²θ = 1