Question

cos⁴A − sin⁴4 A is equal to
(a)2 cos² A + 1
(b)2 cos²A − 1
(c)2 sin² A − 1
(d)2 sin²2 A + 1

Answer 1

Answer:

cos⁴A − sin⁴A is equal to 2cos²A - 1 .

Among the given options option (b) (2cos²A - 1)  is correct.

Step-by-step explanation:

Given : cos⁴A − sin⁴A  

= (cos²A)² − (sin² A)²

= (cos²A + sin²A)  (cos²A − sin²A)

[By using identity , a² - b² =  (a + b) (a - b)]

= 1 × (cos²A − sin²A)

[By using an identity , sin² θ + cos² θ = 1]

= cos²A − sin²A

= cos²A − (1 - cos²A)

[By using  an identity, sin²θ = (1- cos²θ)]

= cos²A − 1 + cos²A

= 2cos²A - 1  

Hence, cos⁴A − sin⁴A is equal to 2cos²A - 1 .

HOPE THIS ANSWER WILL HELP YOU...

 

Answer 2

cos^4 A- sin^4A

(cos^2A + sin^2A)(cos^2A - sin^2A)

cos^2A - sin^2A

2cos^2 - 1

option b