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y= √( (1-sinx)/(1+sinx)) , prove that (d y/dx)+ Sec 2 ((π/4)-x)=0

y=√((1-sinx)/(1+sinx)) , prove that (dy/dx)+Sec2((π/4)-x)=0

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1 Answers

vikas singh
31 Points
8 years ago

Question is wrong !

y=√((1-sinx)/(1+sinx))

1-sinx/1-sinx=

       =   1-cos(90-x)/1+cos(90-x)

       =  1-1+2Sin2(45-(x/2))/1+2cos2(45-(x/2))-1

       =    [tan(45-x/2)]2

 

hence y= [tan2(45-x/2)]1/2

            y= tan (45-x/2)

   dy/dx= sec2(45-x/2)  . {0-1/2}

   dy/dx=  -0.5sec2(45-x/2)

0r        dy/dx+0.5sec2(45-x/2) = 0

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