How do you find the exact value of #cot(v-u)# given that #sinu=-7/25# and #cosv=-4/5#?

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Answer 1 · 2017-08-15T00:30:34

# cot(v-u) = -117/44 #

We have:

# cot(v-u) = 1/tan(v-u) #

Now,

# tan(v-u) = (tanv-tanu)/(1+tanvtanu) #

We are given that #sinu=-7/25 # and #cosv=-4/5#

Using #sin^2A+cos^2A -= 1# we have:

# cos^2u=1-49/625 = 567/625 #
# :. cosu = 24/25 #
# :. tanu = (-7/25)/(24/25) = -7/24 #

Similarly,

# sin^2v=1-16/25 = 9/.25 #
# :. sinv = 3/5 #
# :. tanv = (3/5)/(-4/5) = -3/4 #

And so we can evaluate # tan(v-u)#:

# tan(v-u) = ((-3/4)-(-7/24))/(1+(-3/4)(-7/24)) #
# " " = (-11/24)/(1+7/32) #
# " " = (-11/24)/(39/32) #
# " " = -44/117 #

Hence:

# cot(v-u) = -117/44 #