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Hi, please help me prove an identity..

\(Sin^2xtan^2x+cos^2xtan^2x=1-sec^2x\)

 May 26, 2019
 #1
avatar+107480 
+1

LHS 

factorise and it will fall out to     tan^2 (x )    in just 2 lines

 

RHS

\(1-sec^2x\\ =1-\frac{1}{cos^2x}\\ =\frac{cos^2x-1}{cos^2x}\\ =\)

 

 

You should be able to finish if from there.  wink

 May 26, 2019
 #2
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+1

Dearest Melody, it's juriemagic here...working from my phone....uhm, I made an error..it's supposed be \(1+sec^2x\)

Guest May 26, 2019
 #3
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+1

Melody, no, I am really stuck...please help me...

Guest May 26, 2019
 #4
avatar+107348 
+1

I think it's supposed to be    sec^2 x - 1

 

To see why.....the left hand side  can be factored as

 

tan^2x  (sin^2 x + cos^2 x)  =

 

tan^2 x ( 1)  =

 

tan^2 x

 

But 

 

tan^2x =  sec^2 x - 1      add 1 to both sides

 

tan^2 x + 1  =  sec^2 x      which is an identity

 

 

cool cool cool

CPhill  May 26, 2019
 #5
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+1

Thank you CPhill, I do appreciate it all!

Guest May 26, 2019

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