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anonymous
 one year ago
True or False?
tan^2x= 1+ cos2x / 1cos2x
anonymous
 one year ago
True or False? tan^2x= 1+ cos2x / 1cos2x

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{1\cos^2(x)} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1verify or prove ?

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.0Multiply both sides by 1cos^2 x and simplify , keeping in mind that \[tan(x)=\frac{sin(x)}{cos(x)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It does not specify on the question itself but I would assume proving.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(verify = manipulate 1 side at a time only prove= both sides can be manipulate) this is a traditional interpretation/definition of these words.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1ok, lets just in case verify it. will play 1 side at a time

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{1\cos^2(x)} }\) can you rewrite the bottom ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1use the fact that \(\large\color{black}{ \displaystyle \sin^2(x)+\cos^2(x)=1 }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So you would be able to rewrite the bottem

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, in the fact I just offered, subtract cos^2(x) from both sides, and tell me what you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0From the sin^2(x) one?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, from the sin^2(x)+cos^2(x)=1, there subtract cos^2(x) from both sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin ^{2}(x)=\cos ^{2}(x)+1\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes sin^2(x)=1cos^2(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, we have \(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{1\cos^2(x)} }\) can you rewrite the bottom for me?

Pawanyadav
 one year ago
Best ResponseYou've already chosen the best response.0That is false As 1+cos2x=1+2cos^2x1 =2cos^2x And 1cos2x=1(12sin^2x) =2sin^2x Put these values you will get the answer.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0just put x = pi/4 , you can see how it is false

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When I rearrange this @SolomonZelman, will I be taking the cos^2(x) away from the denominator and onto the numerator? I am not very good at trig

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{1\cos^2(x)} }\) \(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{\sin^2(x)} }\) that is what I meant

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1anyway, i think plugging in value to disprove is valid enough.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1unless u want to go and do it without plug ins

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would I just have to plug in pi/4 to the equation?

Pawanyadav
 one year ago
Best ResponseYou've already chosen the best response.0But that's not a proper method

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well thank you guys for the help and time

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Who said : proving the invalid of an expression by a counterexample is not a proper method?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0That is the MOST proper method to prove something wrong.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \tan^2(x)=\frac{ 1+\cos^2(x) }{1\cos^2(x)} }\) \(\large\color{black}{ \displaystyle \frac{\sin^2x}{\cos^2x}=\frac{ (1+\cos^2x) }{(1\cos^2x)} }\) \(\large\color{black}{ \displaystyle \frac{\sin^2x}{\cos^2x}=\frac{ (1+\cos^2x) }{(1\cos^2x)} }\) \(\large\color{black}{ \displaystyle \sin^2x(1\cos^2x)=\cos^2x(1+\cos^2x) }\) \(\large\color{black}{ \displaystyle \sin^2x\sin^2x\cos^2x=\cos^2x+\cos^2x\cos^2x}\) \(\large\color{black}{ \displaystyle \sin^2x=\sin^2x\cos^2x+\cos^2x+\cos^2x\cos^2x}\) \(\large\color{black}{ \displaystyle \sin^2x=\cos^2x(\sin^2x+1+\cos^2x)}\) \(\large\color{black}{ \displaystyle \sin^2x=\cos^2x(2)}\) \(\large\color{black}{ \displaystyle \sin^2x=2(1 \sin^2x)}\) \(\large\color{black}{ \displaystyle \sin^2x=2 2\sin^2x}\) \(\large\color{black}{ \displaystyle 3\sin^2x=2}\) \(\large\color{black}{ \displaystyle \sin^2x=2/3}\) \(\large\color{black}{ \displaystyle \sin x=\pm\sqrt{2/3}}\) \(\large\color{black}{ \displaystyle x=\sin^{1}\left(\pm\sqrt{2/3}\right)}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1if your definition were to be true for all numbers, then this solution for x would be such that includes all numbers. \(\large\color{black}{ \displaystyle \sin^{1}\left(\pm\sqrt{2/3}\right)}\) is no way a representation of all [real] numbers!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0*Takes a picture for future reference* Thank you for the explanation! This will help me 200x better than before!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1i took everything down piece by piece. it isn't that bad usually though
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