Question

differentiate (tanx+secx)(cotx+cosecx)​

Answer 1

Answer: Ans) (secx + tanx) (secx – cosecx) (cotx + cosecx)

Step-by-step explanation;

Let us take u = (tan x + sec x) and v = (cot x + cosec x)

(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)