i have two precalc questions..help. work needed too. =]?

Question

1) simplify the expression tan^2x - 2tanx+1/1+tan(-x)

2) use an identity to find the exact value of tan(pi/3+pi/4)

Answer 1

1) Simplify the expression.

Please use parentheses. I assume you mean

(tan²x - 2tanx + 1) / [1 + tan(-x)]
= (tanx - 1)² / (1 - tanx)
= -(tanx - 1)² / (tanx - 1)
= -(tanx - 1)
= 1 - tanx
_______________

2) Value the expression.

Use the angle addition formula for tangents.

tan(π/3 + π/4) = [tan(π/3) + tan(π/4)] / [1 - (tan π/3)(tan π/4)]

= [√3 + 1] / [1 - (√3)(1)]

= [1 + √3] / [1 - √3]

= [1 + √3]² / [(1 - √3)(1 + √3)]

= (1 + 2√3 + 3) / (1 - 3)

= (4 + 2√3) / (-2)

= -2 - √3

Answer 2

1)tan(-x)= -tanx
numerator is of the form (a-b)^2 where a=1 and b=tan x
ques becomes (1-tan x)^2/(1-tan x)
=1-tan x

2)tan(a+b)=( tan a + tan b)/(1-tan a *tan b)
=(tan pi/3 +tan pi/4)/(1-tan pi/3 *tan pi/4)
=(sqrt(3) +1 )/(1- sqrt(3)*1)
=(sqrt(3)+1)/1-sqrt(3)