Expert: Sherman D. - 9/29/2008

Question
PLEASE HELP!

#1

tanx+cotx
--------- = secx
cscx       

#2


cos(u-v)
--------- = tanu cosv
cosu sinv


#3

sin(arctan of square root of 3 over 3)

Answer
1.)
(tan(x) + cot(x))/csc(x) = sec(x)
(tan(x) + (1/tan(x)))/(1/sin(x)) = 1/cos(x)
((tan(x)^2 + 1)/tan(x)) * sin(x) = 1/cos(x)
sin(x)((tan(x)^2 + 1)/(sin(x)/cos(x)) = 1/cos(x)
sin(x) * (cos(x)/sin(x))(tan(x)^2 + 1) = 1/cos(x)
cos(x)(((sin(x)/cos(x))^2 + 1) = 1/cos(x)
cos(x)((sin(x)^2 + cos(x)^2)/cos(x)^2) = 1/cos(x)
1/cos(x) = 1/cos(x)

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2.)
cos(u - v)/(cos(u)sin(v)) = tan(u)cos(v)
(cos(u)cos(v) + sin(u)sin(v))/(cos(u)sin(v)) = tan(u)cos(v)
(cos(v)/sin(v)) + (sin(u)/cos(u)) = tan(u)cos(v)
cot(v) + tan(u) = tan(u)cos(v)

was this one written correctly.

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3.)
sin(arctan(sqrt(3)/3))

sin(A) = y/r
tan(A) = y/x
A = arctan(y/x)

sqrt(3)^2 + 3^2 = r^2
3 + 9 = r^2
r = sqrt(12)
r = 2sqrt(3)

sin(A) = sqrt(3)/sqrt(12)
sin(A) = sqrt(3/12)
sin(A) = sqrt(1/4)
sin(A) = (1/2)

therefore

sin(arctan(sqrt(3)/3)) = (1/2)