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