Trig proofs help!

**steelersgirl18** · December 13th 2009, 10:04 PM

Hi! I needed help verifying the following proofs! If anyone wants to contribute by solving either of them, I will greatly appreciate it!

Sin^(4) x - cos^(4) x = 1-2cos^(2) x

and:

sec x - sin x • tan x = cos x

and:

{(cos^(2) x)/(1+ sin x)} -1= -sin x

thank you!

**bigwave** · December 13th 2009, 10:15 PM

here is the first one

$Sin^{4}x - cos^{4} x = 1-2cos^{2} x$

$(sin^2 - cos^2)(sin^2 + cos^2) = sin^2 + cos^2 - 2cos^2$

$<br /> (sin^2 - cos^2)(1) = sin^2 - cos^2$

continue more??

**steelersgirl18** · December 13th 2009, 10:25 PM

Wow! Thank you so much! Yes, can you please show me the other ones?
Also, can you try verifying them by only working on the left side of the equation? I have to do it that way sorry

**bigwave** · December 13th 2009, 10:40 PM

$sec x - sin x tan x = cos x$

get all terms in $sinx$ and $cosx$

$\frac{1}{cosx} - sinx \frac{sinx}{cosx} = cosx$

$\frac{1 - sin^{2}x}{cosx} = cosx$

$\frac{cos^{2}x}{cosx} = cosx$

$cosx = cosx$

--------------------------------------------------------

$\frac{cos^{2}x}{1 + sinx} - 1 = -sinx$

$cos^{2}x = (-sin+1)(1+ sinx)$

or $cos^{2}x = (1-sinx)(1+ sinx) = 1 - sin^{2}x$

$cos^{2}x = cos^{2}x$

**steelersgirl18** · December 13th 2009, 10:52 PM

Originally Posted by bigwave

$sec x - sin x tan x = cos x$

get all terms in $sinx$ and $cosx$

$\frac{1}{cosx} - sinx \frac{sinx}{cosx} = cosx$

$\frac{1 - sin^{2}x}{cosx} = cosx$

$\frac{cos^{2}x}{cosx} = cosx$

$cosx = cosx$

wait a sec.... When you combined the left side to form (1-sin^2x)/(cosx) , aren't you also supposed to multiple the denominators? So would the correct combination be : (1-sin^2x)/(cos^2x) ?

EDIT: nevermind, you're right whoops

**bigwave** · December 13th 2009, 10:57 PM

we are adding 2 fractions not mulitplying
the common denominator is $cosx$

**steelersgirl18** · December 13th 2009, 11:10 PM

One laaaast thing

can you complete the first one but this time only work on the left side? Thank you so much, you're very helpful

**bigwave** · December 13th 2009, 11:34 PM

$sin^{4}x - cos^{4}x = 1-2cos^{2}x$

$(sin^{2}x - cos^{2}x)(sin^{2}x + cos^{2}x) = 1-2cos^{2}x$

$<br /> ((1-cos^{2}x) - cos^{2}x)(1) = 1-2cos^{2}x$

Thread: Trig proofs help!

LinkBack

Thread Tools

Display

Trig proofs help!

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

the last 2

Similar Math Help Forum Discussions

two trig proofs

trig proofs

Trig Proofs

trig proofs

Help with trig proofs.

Search Tags