SOLUTION: Prove that 1 + tanAtanA/2 = tanAcotA/2 -1 = secA

Algebra.Com
Question 552116: Prove that
1 + tanAtanA/2 = tanAcotA/2 -1 = secA
Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!
1 + tan(A)·tan = tan(A)cot - 1 = sec(A)

We will make use of the half angle identities:

tan = , and its reciprocal cot = , also tan(A) =  and sec(A) = 

First we will prove:

1 + tan(A)·tan = sec(A)

1 +  

1 + 

Get an LCD

 + 

Combine fractions over the LCD



Cancel first and third terms on top:





Cancel the sines:





sec(A)

---------------------------------

Next we will prove:

tan(A)·cot - 1 = sec(A)

 - 1 

 - 1

Get an LCD

 - 

Combine fractions over the LCD



Distribute:



Rearrange:



Use identity sin²(A)+cos²(A)=1



Cancel 1-cos(A)'s





sec(A)

Edwin
RELATED QUESTIONS

1. Prove that (1-cosA) (1-secA) = tan A sinA 2. Prove that secA (1-sinA) (secA+tanA)... (answered by mananth)
Prove that the equations are identities.... (answered by lwsshak3)
prove that sinA*secA/tanA=1 (answered by richard1234)
How does one prove that... (answered by stanbon,josgarithmetic)
SecA-tanA.secA=1/secA (answered by Alan3354)
Prove that : 1. (cscA-1)/(cscA+1) = (1-sinA)/(1+sinA) 2. (secA/cscA)+(sinA/cosA) =... (answered by Edwin McCravy)
1/secA-tanA =secA+tanA (answered by stanbon)
(secA+tanA)(secA-tanA)=1 (answered by Alan3354)
Prove that: 1 + cos A/ 1 - cos A = tan²A/(secA -... (answered by kapilsinghi)