CBSE Class 12-science Answered
integrate: dx/tanx+cotx+secx+cosecx
Asked by Akshansh prasad | 17 Sep, 2013, 03:29: PM
Expert Answer
let A = Tanx+Cotx+Secx+Cosecx
A = (Sinx/Cosx)+(Cosx/Sinx)+(1/Cosx)+(1/Sinx)
= (Sinx^2+Cosx^2+Sinx+Cosx)/Sinx.Cosx
= (1 + Sinx+Cosx)/Sinx.Cosx
Multiply by (Sinx+Cosx-1) in denominator and numerator
A = (Sinx+Cosx+1)(Sinx+Cosx-1) / (Sinx.Cosx)(Sinx+Cosx-1)
= (Sinx^2+Cosx^2+2Sinx.Cosx-1) / (Sinx.Cosx)(Sinx+Cosx-1)
= (1+2Sinx.Cosx-1) / (Sinx.Cosx)(Sinx+Cosx-1)
= (2Sinx.Cosx) / (Sinx.Cosx)(Sinx+Cosx-1)
= 2 / (Sinx+Cosx-1)
I = integrate dx/(Tanx+Cotx+Secx+Cosecx)
I = integrate dx/A
I = integrate (Sinx+Cosx-1) dx/2
I = (-Cosx + Sinx -x)/2 + C
Answered by | 19 Sep, 2013, 10:03: AM
Concept Videos
CBSE 12-science - Maths
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by atulmishra514 | 26 Jan, 2024, 10:15: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by aalavarshitha2005 | 21 Jan, 2024, 05:28: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by atharvaparkar04 | 17 Dec, 2023, 12:59: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by shashinayaka032 | 05 Dec, 2023, 12:46: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by manyarajawat1 | 06 Nov, 2023, 05:03: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by ps9680677 | 26 Oct, 2023, 11:47: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by manasvichandel49 | 19 Oct, 2023, 08:53: AM
ANSWERED BY EXPERT