Question

prove the trigonometric identity:
cos4A - cos2A = sin4A - sin2A​

Answer 1

Answer:

and then we have listed several

Answer 2

(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