evaluate... the integral.. 1/5cosx-12sinx dx
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step:- 5cosx-12sinx=13 {5/13cosx-12/13sinx}=13 {cos@cosx-sin@ sinx}=13cos(x-@)
where sin@=12/13
cos@=5/13
@=tan^-1 (12/5)
step 2:- integrate 1/cos(x-@) dx
integrate sec (x-@) dx
now use
secx.dx =ln(secx+tanx)+c
i.e sec (x-@) dx=ln{sec (x-@)+tan (x-@)}
where sin@=12/13
cos@=5/13
@=tan^-1 (12/5)
step 2:- integrate 1/cos(x-@) dx
integrate sec (x-@) dx
now use
secx.dx =ln(secx+tanx)+c
i.e sec (x-@) dx=ln{sec (x-@)+tan (x-@)}
abhi178:
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