Question 600688
cot(x) = 5/12


cot^2(x) = (5/12)^2


cot^2(x) = 25/144


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Now use the identity 1+cot^2(x) = csc^2(x)


1+cot^2(x) = csc^2(x)


1+25/144 = csc^2(x)


169/144 = csc^2(x)


csc^2(x) = 169/144


csc(x) = sqrt(169/144) ... See <font color="red">note</font> below


csc(x) = sqrt(169)/sqrt(144)


csc(x) = 13/12


<font color="red">Note</font>: Because cos(x) > 0 and cot(x) = cos(x)/sin(x), this means that sin(x) > 0 as well (to keep cot(x) positive). This forces csc(x) > 0 (because csc(x) = 1/sin(x))



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<font color="red">Answer:</font> So the answer is csc(x) = 13/12