trig (1 Viewer)

[vizman]

i've got a couple of questions i can't seem to grasp. thanks in advance

1. Prove that cot(A+B) = cotAcotB+1 / cotAcotB

2. Prove that 1-cosA / 1+cosA = tan^2 A/2

 

[FinalFantasy]

i've got a couple of questions i can't seem to grasp. thanks in advance

1. Prove that cot(A+B) = cotAcotB+1 / cotAcotB

2. Prove that 1-cosA / 1+cosA = tan^2 A/2

1. cot(A+B)=cos(A+B)\sin(A+B)=[cosAcosB-sinAsinB]\[sinAcosB+cosAsinB]

1\tan(A+B)=(1-tanAtanB)\(tanA+tanB)
=(cosAcosB-sinAsinB)\(sinAcosB+sinBcosA)

2.(1-cosA)\(1+cosA)=(1-[1-2sin(A\2)])\(1+2cos(A\2)-1)
=tan(A\2)

 

[vizman]

thnx mate.

 

[FinalFantasy]

oh with that first question... i just realised i just did lots of stuff and its not wat im meant to do... hehehe

 

[Mountain.Dew]

oh with that first question... i just realised i just did lots of stuff and its not wat im meant to do... hehehe

agreed, the question can be done in terms of tanA and tanBs, knowing that cot(A) = 1/tan(A)

 

[icycloud]

I think the first question is a typo.

cot(A+B) does not equal (cotAcotB+1 )/ cotAcotB

cot(A+B) = 1/tan(A+B)
= (1-tanA tanB)/(tan A + tan B)<-- divide top and bottom by tanAtanB
= (cotA cotB - 1) / (cotB + cot A)
#

 

[Riviet]

I think the first question is a typo.

cot(A+B) does not equal (cotAcotB+1 )/ cotAcotB

cot(A+B) = 1/tan(A+B)
= (1-tanA tanB)/(tan A + tan B)<-- divide top and bottom by tanAtanB
= (cotA cotB - 1) / (cotB + cot A)
#

Hmm, I was thinking of that too earlier today. It was the -1 that put me off when I looked at what was required to be proved.

 

[vizman]

its a review question from the AML Understanding Maths Year 11 Ext.1 and it definately says +1, or course it could be a typo