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∫dx/[sin(x/2)+Cos(x/2)]=?

∫dx/[sin(x/2)+Cos(x/2)]=?

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

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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