Question

cos⁴A − sin⁴A is equal to 

A. 2 cos²A + 1 

B. 2 cos²A − 1 

C. 2 sin²A − 1 

D. 2 sin²A + 1

Answer 1

To find: cos⁴A – sin⁴A 

Consider cos⁴A – sin⁴A = (cos²A)² – (sin²A)² 

∵ a² – b² = (a – b) (a + b)

∴ cos⁴A – sin⁴A = (cos²A)² – (sin2 A)² 

= (cos²A – sin²A) (cos²A + sin²A) 

= (cos²A – sin²A) [∵ cos²A + sin²A = 1] 

= cos²A –(1 – cos²A) [∵ sin²A = 1 – cos²A] 

= cos²A – 1 + cos²A = 2 cos²A – 1

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