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integration(1/(tanx+cotx+secx+cscx))dx=?

integration(1/(tanx+cotx+secx+cscx))dx=?

Grade:12th pass

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
integral (1/sinx/cosx+cosx/sinx+1/cosx+1/sinx)dx
=integral(sinxcosx)/(1+sinxcosx)dx
=integral sinx cosx/2cos^(x/2)+2 sin(x/2)cos(x/2)dx
=integral sinxocsx/2cos(x/2)(cos(x/2)+sin(x/2) dx
integral2 sin(x/2)cos(x/2) cosx/2cos(x/2)(cosx+sinx) dx
=integral sin(x/2). (cos(x/2)-sin(x/2))(cos(x/2)+sin(x/2))/cos(x/2)+sin(x/2) dx
=integral sin(x/2)cos(x/20 dx-integral sin^2(x/2) dx
=1/2 Integral sinxdx-1/2 integral (1-cosx) dx
=-1/2 cosx-1/2[x-sinx]
=-(cosx)/2-x/2+(sinx)/2 Ans.
Thanks & Regards
Rinkoo Gupta
AskIITians Fcaulty
mamillapelly bhagath
33 Points
7 years ago
Sir i can`t understand 2 step plz give explanation

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