Question

Cot x + cosecx= 5 then what is the value of. Cos x from 5/12, 12/13,5/13,1/3 or1/12?

Answer 1

cotx+cosecx=5
cosx/sinx+1/sinx=5
cosx+1=5sinx

Answer 2

given cotx+cosecx=5.............(i)

we know from identities cosec²x-cot²x=1

 ⇒(cosecx+cotx)(cosecx-cotx)=1

cosecx-cot= 1/5 ..................(ii)

solving (i) and (ii),we get 
2cosecx = 26/5

cosecx=13/5

∴ sinx = 5/13

cosx=√1-(5/13)²

cosx = 12/13