Evaluate cos⁴A-sin²A.
Answers
Answer:
Cos 4a-cos2a=sin4a-sin2a
ANSWERS
cos 4 A - Cos2A
= (cos2A)2 - (cosA)2
= (1- sin2A)2 - cos2A
= 1 + sin4A - 2sin2A -( 1- sin2A)
=1+ sin4A - 2 sin2A -1 + sin2A
=sin4A - sin2A
since LHS = RHS
hence proved.
Step-by-step explanation:
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Answer:
(cos^4A)-cos^2A=
=(cos^2A)^2-(cos^2A)
=cos^2A(cos^2A-1)
= -cos^2A(1-cos^2A)
= -cos^2A*sin^2A (By using the identity sin^2A+cos^2A=1) ———————- 1
Now,
sin^4A-sin^2A
=(sin^2A)^2-sin^2A
=sin^2A(sin^2A-1)
=-sin^2A(1-sin^2A)
= - sin^2A*cos^2A(Again using the identity sin^2A+cos^2A=1)
= -cos^2A*sin^2A ———————- 2
From 1 and 2
cos^4A-cos^2A=sin^4A-sin^2A
Hence proved
Step-by-step explanation:
#Hope you have satisfied with this answer.