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Help in Trig CIE Maths A2 Pure

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masterof13:
Hi all!
Small problem in Trigonometry, the question is "Prove that cos4x-4cos2x+3 equals 8sin4x."
I would like a step by step answer if possible!  ::)
Thanks in advance! :)

Amr Fouad:
in 5 mins

Amr Fouad:
Cos4x-4cos2x+3

Lets break it into parts:

1)   Cos4x:
= cos (2x+2x)
Cos2xcos2x-sin2xsin2x
(cos^2x-sin^2x)^2 – (2sinxcosx)^2
(1-2sin^2 x)^2  - 4sin^2 x cos^2 x
(1-2sin^2 x)(1-2sin^2 x) – 4sin^2 x(1-sin^2 x)
1-4sin^2 x+ 4sin^4 x-4sin^2 x + 4sin^4 x
=8sin^4 x-8sin^2 x +1

2)   -4cos2x:

-4(cos^2 x –sin^2 x)
-4(1-2sin^2 x)

=-4+8sin^2 x

3)   +3
Therfore, combining all parts gives us:
8sin^4 x-8sin^2x+1-4+8sin^2x+3
Which equals to: 8sin^4 x..

Got it?

masterof13:
OMG THANK YOU VERY VERY MUCH!!  :)
It helped alot!

Amr Fouad:
glad i helped :)

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