Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If Ι n = 
, snd Ι n = 
(sinx + cosx) n–1 (sinx – cosx) + 
Ι n–2 then k =
Text Solution
Verified by ExpertsThe correct answer is:
B
Ι n = 
⇒ Ι n = (sinx + cosx) n–1 (–cosx + sinx) – (n – 1) 
⇒ Ι n = (sinx + cosx) n–1 (sinx – cosx)+ (n – 1)(sinx + cosx) n–2 (2 – (sinx + cosx) 2 )dx
⇒ Ι n = (sinx + cosx) n–1 (sinx – cosx) + 2(n – 1) Ι n–2 – (n – 1) Ι n
⇒ n Ι n = (sinx + cosx) n–1 (sinx – cosx) + 2(n – 1) Ι n–2
⇒ Ι n = 
(sinx + cosx) n–1 (sinx – cosx) + 
Ι n–2
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