How do you find the exact value of #cot(u+v)# given that #sinu=5/13# and #cosv=-3/5#?

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Answer 1 · 2018-01-31T15:54:07

I tried this:

Consider that:
#cot(u+v)=cos(u+v)/sin(u+v)#
but:

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so we can write:

#cot(u+v)=cos(u+v)/sin(u+v)=[cos(u)cos(v)-sin(u)sin(v)]/[sin(u)cos(v)+sin(v)cos(u)]#

we also know that:

#sin^2x+cos^2x=1#

so we can write:

#cos(u)=+-sqrt(1-sin^2(u))#
and:
#sin(v)=+-sqrt(1-cos^2(v))#

that can be evaluated using the given values in the problem.

You can now evaluate #cot(u+v)#!