tri probs (1 Viewer)

[Aznmichael92]

i posted this question in the wrong section so I am reposting it. Can someone help me with this question.

Prove cos 2@ = 1- tan^2 @/ 1 + tan^2 @

hence show that

tan67*30' = 1 + root2

thanks for the help

 

[bored of sc]

cos2@ = (1-tan²@) / (1+tan²@)

RHS = [1-(sin²@/cos²@)] / [1+(sin²@/cos²)] ----- express tan as sin/cos
= [(cos²@-sin²@)/cos²@] / [(cos²@+sin²@)/cos²@] ----- treat numerator fraction as one and create a common denominator of cos²@, do this for the denominator fraction too
= cos²@ - sin²@ ---- cancel cos²@ and recognise sin²@+cos²@ = 1 {fundamental identity}
= cos2@
= LHS

 

[friction]

how do you get the 2s like that to go to squares ??

BTW very nice concise clear answer

 

[bored of sc]

cos135 = (1-tan²67.5) / (1+tan²67.5)

Substitute in tan67.5 as 1 + rt2.

RHS = [1 - (1+rt2)²] / [1 + (1+rt2)²]

= [1-(1+2rt2+2)] / [1+(1+2rt2+2)]

= (-2-2rt2) / (4+2rt2)
= (-1-rt2) / (2+rt2)

rationalise denominator

= -rt2/2

irrationalise denominator i.e. multiply by rt2/rt2

= -2/2rt2
= -1/rt2
= -cos45
= cos135
= LHS

 

[bored of sc]

how do you get the 2s like that to go to squares ??

BTW very nice concise clear answer

without the gaps between do

[ s u p ] 2 [ / s u p ]

 

[Aznmichael92]

loves you all for helping I AM SO GRATEFUL!

 

[adnan91]

cos135 = (1-tan²67.5) / (1+tan67.5)

Substitute in tan67.5 as 1 + rt2.

RHS = [1 - (1+rt2)²] / [1 + (1+rt2)²]

= [1-(1+2rt2+2)] / [1+(1+2rt2+2)]

= (-2-2rt2) / (4+2rt2)
= (-1-rt2) / (2+rt2)

rationalise denominator

= -rt2/2

irrationalise denominator i.e. multiply by rt2/rt2

= -2/2rt2
= -1/rt2
= -cos45
= cos135
= LHS

Im sorry but ur method is incorrect, you may got the answer but how u proved is wrong. you cannot use the thing ur trying to prove in ur proof so u cannot use tan^2(67.5)=1 + rt2. Let @=67.5 and work from there u cannot substitute tan^2(67.5)= 1 + rt2

 

[bored of sc]

Im sorry but ur method is incorrect, you may got the answer but how u proved is wrong. you cannot use the thing ur trying to prove in ur proof so u cannot use tan^2(67.5)=1 + rt2. Let @=67.5 and work from there u cannot substitute tan^2(67.5)= 1 + rt2

But the question says 'show'. Okay, maybe I don't know what I'm talking about. :S

 

[Timothy.Siu]

that seems correct, it didn't say to prove...i dont know though.

 

[Aznmichael92]

oh i see prove and show are two different things

 

[bored of sc]

oh i see prove and show are two different things

Yeah.

 

[bored of sc]

What is the difference? I thought it was just which way you work from like LHS or RHS but reading this it seems to be more than that.

I thought with 'show' you can assume that certain things are already true while with prove you have to use other bits of information to demonstrate that something is true.