Differentiate:
(tan x + sec x) (cot x + cosec x)
To find: Differentiation of (tan x + sec x) (cot x + cosec x)
Formula used: (i) (uv)′ = u′v + uv′ (Leibnitz or product rule)
(ii)
(iii)
(iv)
(v)
Let us take u = (tan x + sec x) and v = (cot x + cosec x)
Putting the above obtained values in the formula:-
(uv)′ = u′v + uv′
[(tan x + sec x) (cot x + cosec x)]’
= [secx (secx + tanx)] × [(cot x + cosec x)] + [(tan x + sec x)] × [-cosecx (cosecx + cotx)]
= (secx +tanx) [secx(cotx + cosecx) - cosecx(cosecx + cotx)]
= (secx + tanx) (secx – cosecx) (cotx + cosecx)
Ans) (secx + tanx) (secx – cosecx) (cotx + cosecx)