Question

.
Prove that cos 4x = 1 - 8 sin^2 x cos^2 x​

Answer 1

Answer:

This answer. please check

Answer 2

Answer:

cos 4 x = 1 - 8 sin² x cos² x [ Proved ]

Step-by-step explanation:

Given :

cos 4 x = 1 - 8 sin² x cos² x

L.H.S. = cos 4 x

= > cos 2 ( 2 x )

Using multiple angle formula :

i.e. cos 2 x = 2 cos² x - 1

= > cos 2 ( 2 x )

= > cos 2 ( 2 x )

= > 2 ( 2 cos² 2 x - 1 ) - 1

= > 2 ( 2 cos² x - 1 )² - 1

= > 2 ( 4 cos⁴ x - 4 cos² x + 1 ) - 1

= > 8 cos⁴ x - 8 cos² + 2 - 1

= > 1 - 8 cos² x ( 1 - cos² x )

We know :

1 - cos² x = sin² x

= > 1 - 8 cos² x . sin² x

Since L.H.S. = R.H.S

Hence proved.