integrate 1/1-tanx
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Naveen Sharma 8 years, 3 months ago
Ans. ∫11−tanxdx
=>∫11−sinxcosxdx
=>∫cosxcosx−sinxdx
Multiply and Divide By 2, We Get
=>12∫2cosxcosx−sinxdx
=>12∫2cosx+sinx−sinxcosx−sinxdx
=>12∫(cosx+sinx)+(cosx−sinx)cosx−sinxdx
=>12∫(cosx+sinx)cosx−sinxdx+12∫(cosx−sinx)cosx−sinxdx
=>12∫(cosx+sinx)cosx−sinxdx+12∫dx
Put (cos x - sin x) = t, then
(-sin x - cos x)dx = dt or -(cos x +sin x) dx = dt
=>12∫−dtt+12∫dx
=>−12logt+12x+C
=>−12log(cosx−sinx)+12x+C
1Thank You