If sec x + tan x = 5 and cosec y - cot y = 1/3, then find the value of (sec x + cosec y) - tan x - cot y ).

3.2

We are given :-

secx + tanx = 5  & cosecy - coty = \(\frac{1}{3}\)

{ we know, sec²x - tan²x = 1  so , secx - tanx = \(\frac{1}{secx + tanx}\)

& cosec²x - cot²x = 1  so , cosecx - cotx = \(\frac{1}{cosecx + cotx}\) }

So, secx - tanx = \(\frac{1}{5}\)  & cosecx + cotx = 3

Now,

(sec x + cosec y) - tan x - cot y )

= ( secx - tanx ) + ( cosecx - coty )

= \(\frac{1}{5}\) + 3

= \(\frac{16}{5}\)

= 3.2