Question

Complete the identity. sin4x - cos4x = ?

A. 1 - 2cos2 x

B. 1 - 2sin2 x

C. 1 + 2sin2 x

D. 1 + 2cos2 x

Answer 1

@UnkleRhaukus @jim_thompson5910

Answer 2

What do you mean by sin4x... do you mean

\[\sin^{4} x\]
?

Answer 3

yes

Answer 4

sin^4x - cos^4x = ?

A. 1 - 2cos^2 x

B. 1 - 2sin^2 x

C. 1 + 2sin^2 x

D. 1 + 2cos^2 x

Answer 5

Well, it's A, you want me to elaborate? :)

Answer 6

yes plz

Answer 7

\[(\sin ^{2}x-\cos ^{2}x)(\sin ^{2}x+\cos ^{2}x)\]
\[(\sin ^{2}x-\cos ^{2}x)(1) \implies (1-\cos ^{2}x-\cos ^{2}x)\implies (1-2\cos ^{2}x)\]

Answer 8

That ^

Answer 9

the identity used is \[\sin ^{2}x+\cos ^{2}x=1\]

Answer 10

sin^4x - cos^4x

(sin^2x)^2 - (cos^2x)^2

(sin^2x-cos^2x)(sin^2x+cos^2x)

(sin^2x-cos^2x)(1)

sin^2x-cos^2x

(1-cos^2x)-cos^2x

1-cos^2x-cos^2x

1-2cos^2x

So

sin^4x - cos^4x = 1-2cos^2x for all values of x

Answer 11

@nitz i dont get this part