How do you verify $8sin²xcos²x = 1-cos^4(x)$ ?

Question

How do you verify $8sin²xcos²x = 1-cos^4(x)$ ?

1 Answer

Impact of this question

1601 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-03T17:02:10

This can not be proven because it is not in general true.

As a counter example, consider $x=pi/4$

$color(white)("XXXX")$ $sin(x) = 1/sqrt(2)$
$color(white)("XXXX")$ $color(white)("XXXX")$ $sin^2(x) = 1/2$
$color(white)("XXXX")$ $cos(x) = 1/sqrt(2)$
$color(white)("XXXX")$ $color(white)("XXXX")$ $cos^2(x) = 1/2$
$color(white)("XXXX")$ $color(white)("XXXX")$ $cos^4(x) = 1/4$

$8 sin^2xcos^2x = 8 * 1/2*1/2 = 2$

$1-cos^4(x) = 1- 1/4 = 3/4$

$8 sin^2xcos^2x != 1-cos^4x$

Science

Math

Humanities

... and beyond

How do you verify $8sin²xcos²x = 1-cos^4(x)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you verify 8sin²xcos²x = 1-cos^4(x)8sin²xcos²x = 1-cos^4(x)?

1 Answer

Related questions

Impact of this question

How do you verify $8sin²xcos²x = 1-cos^4(x)$ ?