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Mathematics 81 Online
OpenStudy (anonymous):

Verify The Identity Cos(x)+Sin(x)Tan(x)=Sec(x) Can someone please help explain to me how to verify an identity?

OpenStudy (anonymous):

try drawing a triangle and label the ratios and go from there....

OpenStudy (anonymous):

Ok.. I guess I'm confused by what ratios? No numbers were given. I know you probably would start with the left side of this equation (maybe divide each side by tan(x)?)

OpenStudy (anonymous):

use this, and create your ratios...Example Sin=b/c http://3.bp.blogspot.com/_kjNvt_oqTsE/TORcXMO_H6I/AAAAAAAAACo/CbLIh4wjhaI/s1600/Image289.gif

OpenStudy (anonymous):

put it in those terms and it should be easier for you to prove...

OpenStudy (anonymous):

Proving a proof cannot be done using what is given, it must be changed to new terms...Just like the definition of a word can't include the word....

OpenStudy (anonymous):

does it matter where I put each term?

OpenStudy (anonymous):

put them in the order of the identity...So, Cosx becomes (a/c) etc...

OpenStudy (anonymous):

oh ok...

OpenStudy (anonymous):

so I have cosx=a/c sinx=b/c and tanx= c/?

OpenStudy (anonymous):

the tangent is what? Its the opposite side/adjacent side... (b/a)

OpenStudy (anonymous):

So...(a/c)+(b/c)(b/a) and solve...

OpenStudy (anonymous):

OHHH ok! and I want it to equal secx which is equal to what? a/b?

OpenStudy (anonymous):

OHHH ok! and I want it to equal secx which is equal to what? a/b?

OpenStudy (anonymous):

i have confused you, and I'm sorry...You need to see that Tangent equals (sin/cos) and make that substitution.

OpenStudy (anonymous):

Once you see that, then the fractions become easier to work, because they are impossible to work without that substitution.

OpenStudy (anonymous):

ok so i understand that now...

OpenStudy (anonymous):

Completely ignore the answer Secant side of the equation, and solve the fractional problem...and you'll determine what secant is in terms of fractions, which is what they want....

OpenStudy (anonymous):

So, basically, this... sin x tan x + cos x = sin x (sin x / cos x) + cos x = ( sin^2(x) / cos x ) + cos x = [ sin^2(x) + cos^2(x) ] / cos x = 1 / cos x = sec x

OpenStudy (anonymous):

Alright so I was close on my paper... I think I just mixed up the terms. Therefore this is an identity. Thank you!

OpenStudy (anonymous):

Ok one more Question...does theta basically resemble the x in the previous problem?

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