Question

Prove the following identities :
sin4 A – cos4 A = 2 sin2 A – 1 = 1 – 2 cos2 A = sin2 A – cos2 A

Answer 1

2Sin3*Sin1 = 2Cos3*Sin1

tan3 = -1

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Answer 2

QUESTION:

prove that

sin⁴A - cos⁴A = 2sin²A - 1 = 1 - 2sin²A = sin²A - cos²A

USED FORMULAS:

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

sin²A + cos²A = 1

sin²A = 1 - cos²A

cos²A = 1 - sin²A

ANSWER:

(sin²A)² - (cos²A)²

= (sin²A + cos²A)(sin²A - cos²A)

= 1(sin²A - cos²A)

= sin²A - cos²A ✓✓

______________________

= sin²A - (1 - sin²A)

= sin²A - 1 + sin²A

= 2sin²A - 1 ✓✓

______________________

= (1 - cos²A) - cos²A

= 1 + cos²A + cos²A

= 1 + 2cos²A ✓✓