precalculus
posted by anonymous on .
For each of the following determine whether or not it is an identity and prove your result.
a. cos(x)sec(x)sin^2(x)=cos^2(x)
b. tan(x+(pi/4))= (tan(x)+1)/(1tan(x))
c. (cos(x+y))/(cos(xy))= (1tan(x)tan(y))/(1+tan(x)tan(y))
d. (tan(x)+sin(x))/(1+cos(x))=tan(x)
e. (sin(xy))/(sin(x)cos(y))=1cot(x)tan(y)
f. sin(x)sin(y)=(1/2)[cos(xy)cos(x+y)]

a
1  s^2 = c^2
yes
s^2+c^2 = 1
b
t(x+pi/4) = (t x + 1)/(1t x)
yes
c
t x t y = s x /c x * s y/c y
so on the right we have
[1  (s x s y / c x c y) ] / [ 1 + ( s x s y /c x c y) ]
[c x c y  s x s y] / [c x c y + s x s y]
which is indeed
c(x+y)/c(xy)
so yes
d I am getting bored. I think you cn see the plan.