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∫dx/[sin(x/2)+Cos(x/2)]=?
I = dx/[ sinx/2 + cosx/2 ]
=dx/21/2[(sinx/2)(1/21/2) + (cosx/2)(1/2)1/2] (multiplying dividing by 21/2)
=dx/21/2[(sinx/2)(cospi/4) + (cosx/2)(sinpi/4)]
=dx/21/2[sin(x/2+pi/4)] (sina+b = sinacosb+cosasinb)
=cosec(x/2+pi/4)dx/21/2
=log[cosec(x+pi/4) -cot(x+pi/4)] + c
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