I keep getting the wrong answer with half angle identity

[cotfw]

I'm supposed to find the exact value of this:

tan(67.5) //in degrees


I tried using the tan(a/2) = [1-cosA]/sinA formula, and this got me 3/2 + √2 as an answer. But the book says it's 1+√2 . I can't quite figure out how they got that though. Do you know what I'm doing wrong?

 

[Deleted member 4993]

I'm supposed to find the exact value of this:

tan(67.5) //in degrees


I tried using the tan(a/2) = [1-cosA]/sinA formula, and this got me 3/2 + √2 as an answer. But the book says it's 1+√2 . I can't quite figure out how they got that though. Do you know what I'm doing wrong?

Correct ... but

How did you get that? Please show work.

Book's answer is correct.

 

[cotfw]

Correct ... but

How did you get that? Please show work.

Book's answer is correct.

Ok I tried it again and I got it right, but I am still confused, because I tried to solve it using this alternate formula:

tan(a/2) = +/-√(1-cosA)/√(1+cosA)

When I try it with this formula, my work proceeds like this:

I know that tan 67.5 will be positive, so I only look for the positive square root. That gives me √(2+√2)/√(2-√2). When I check to see if this equals the book's answer, it doesn't.

√(2+√2)/√(2-√2) squared should equal √2 + 1 squared.

(2+√2)/(2-√2) = 3 + 2√2

Multiplying both sides by 2-2√2 gives me:

(2-√2) = -2 -2√2

Which I can already see is not equal. Do you know what I'm doing wrong?