Q. 6

cos4 A sin4 A is equal to
A. 2 cos2 A + 1

B. 2 cos2 A 1

C. 2 sin2 A 1

D. 2 sin2 A + 1

Answer :

To find: cos4 A – sin4 A

Consider cos4 A – sin4 A = (cos2 A)2 – (sin2 A)2


a2 – b2 = (a – b) (a + b)


cos4 A – sin4 A = (cos2 A)2 – (sin2 A)2


= (cos2 A – sin2 A) (cos2 A + sin2 A)


= (cos2 A – sin2 A) [ cos2 A + sin2 A = 1]


= cos2 A – (1 – cos2 A) [ sin2A = 1 – cos2A]


= cos2 A – 1 + cos2 A = 2 cos2 A – 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.