[SOLVED] Verify that each trigonometric equation is an identity.

**somanyquestions** · March 21st 2010, 07:42 PM

how do i prove (sin^4 x)-(cos^4 x)= (2sin^2x)-1

**pickslides** · March 21st 2010, 07:48 PM

Originally Posted by somanyquestions

how do i prove (sin^4 x)-(cos^4 x)= (2sin^2x)-1

$\sin^4 x-\cos^4 x$

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

$(\sin^2 x)^2-(1-\sin^2 x)^2$

Expand....

**somanyquestions** · March 21st 2010, 07:51 PM

Originally Posted by pickslides

$\sin^4 x-\cos^4 x$

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

$(\sin^2 x)^2-(1-\sin^2 x)^2$

Expand....

?? expand?

**Stroodle** · March 21st 2010, 08:05 PM

$\left [\sin^2 (x)\right ]^2-\left [ 1-\sin^2 (x)\right ]^2$

$=\left [sin^2(x)+(1-sin^2(x))\right ]\left [sin^2(x)-(1-sin^2(x))\right]$

**somanyquestions** · March 21st 2010, 08:13 PM

Originally Posted by Stroodle

$\left [\sin^2 (x)\right ]^2-\left [ 1-\sin^2 (x)\right ]^2$

$=\left [sin^2(x)+(1-sin^2(x))\right ]\left [sin^2(x)-(1-sin^2(x))\right]$

i have no idea what that means but this is what i did:

sin4 x -(1- 2sin^2 x + sin4 x)
sin4 x - 1+ 2sin^2 x - sin4 x
sin4 x's cancel out

-1+2sin^2 x = 2sin^2 x-1

**pickslides** · March 21st 2010, 08:16 PM

Originally Posted by somanyquestions

?? expand?

$(\sin^2 x)^2-(1-\sin^2 x)^2$

$(\sin^2 x)^2-(1-\sin^2 x)(1-\sin^2 x)$

$(\sin^2 x)^2-(1-2\sin^2 x+(\sin^2 x)^2)$

$(\sin^2 x)^2-1+2\sin^2 x-(\sin^2 x)^2$

finish...

**Stroodle** · March 21st 2010, 08:17 PM

That works too

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