Q. If `y =` `log{tan(pi/4 + x/2)}` , show that  `dy/dx` - `sec x` = 0.

Expert Answers
justaguide eNotes educator| Certified Educator

The function `y = log(tan(pi/4 + x/2))` .

`dy/dx = (1/(tan(pi/4 + x/2)))*sec^2(pi/4 + x/2)*(1/2)`

= `((cos(pi/4 + x/2))/(sin(pi/4 + x/2)))*sec^2(pi/4 + x/2)*(1/2)`

= `(1/(sin(pi/4 + x/2)))*sec (pi/4 + x/2)*(1/2)`

= `1/(sin(pi/4 + x/2)*cos(pi/4 + x/2)*2)`

= `1/(sin(2*(pi/4 + x/2)))`

= `1/(sin(pi/2+x))`

= `1/(cos x)`

= sec x

`dy/dx - sec x = 0`

If `y = log(tan(pi/4 + x/2))` , `dy/dx - sec x = 0`

 

 

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