Ext 1 Half yearly question (1 Viewer)

[fishbulb]

Prove that:
Cos2a = (1-tan^2a)/(1+tan^2a)


This was my proof, tell me if its ok please.
t = tan(a/2)

Cosa = (1-t^2)/(1+t^2)
but a = 2a

therefore cos2a = (1-tan^2a)/(1+tan^2a) as t = tan(2a/2) = tan(a)

Thanks

 

[lyounamu]

Prove that:
Cos2a = (1-tan^2a)/(1+tan^2a)


This was my proof, tell me if its ok please.
t = tan(a/2)

Cosa = (1-t^2)/(1+t^2)
but a = 2a

therefore cos2a = (1-tan^2a)/(1+tan^2a) as t = tan(2a/2) = tan(a)

Thanks

My working out is like the followings:

L.H.S = Cos 2a = cos^2 a - sin^2 a
= 1/sec^2 a - sin^2 a/cos^2 a x cos^2 a
= 1/sec^2 a - tan^2 a/sec^2 a
= 1- tan^2 a/sec^2 a
= 1 - tan^2 a/1 + tan^2 a (since tan^2 a + 1 = sec^2 a)
= R.H.S

I want to redeem myself as I got one question wrong in other thread. :uhhuh:

 

[lyounamu]

Prove that:
Cos2a = (1-tan^2a)/(1+tan^2a)


This was my proof, tell me if its ok please.
t = tan(a/2)

Cosa = (1-t^2)/(1+t^2)
but a = 2a

therefore cos2a = (1-tan^2a)/(1+tan^2a) as t = tan(2a/2) = tan(a)

Thanks

You should have said that t = tan a not t= tan a/2

And you work from there.

Let t = tan a
Therefore, LHS = Cos 2a = 1-t^2 / 1+t^2
= 1 - tan^2 a / 1 +tan^2 a = RHS

 

[tacogym27101990]

回复: Ext 1 Half yearly question

what do u mean that a = 2a??

 

[Trebla]

You technically cannot say "but a = 2a", because this implies a = 0.
A better way to say it is "replace a with 2a" because a, 2a represent what are called "dummy" variables.
Another way is to simply use another name e.g. t = tan (b/2) and let b = 2a

 

[lyounamu]

Re: 回复: Ext 1 Half yearly question

what do u mean that a = 2a??

He got it wrong.

 

[tacogym27101990]

回复: Ext 1 Half yearly question

o ok i understand what he meant now

woulda bin better to use a different pronumeral =]

 

[fishbulb]

I didn't actually write "a = 2a", i just put it in this thread to make it more obvious.
I got it wrong because the teacher wanted it done a different way, without t results for some reason. His method was about 10 steps longer than mine.

 

[lyounamu]

I didn't actually write "a = 2a", i just put it in this thread to make it more obvious.
I got it wrong because the teacher wanted it done a different way, without t results for some reason. His method was about 10 steps longer than mine.

I put up two answers to that question. Have a look.

 

[fishbulb]

I put up two answers to that question. Have a look.

Thanks mate, i like the second one better. I'll see what my teacher says.