Saved Bookmarks
| 1. |
y = \log \sqrt { \frac { 1 + \sin x } { 1 - \sin x } } , \text { show that } \frac { d y } { d x } = \sec x |
|
Answer» y=log√(1+sinx)(1-sinx)/(1-sinx)(1-sinx)y=log√(1-sin^2x)/(1-sinx)^2y=log(cosx)/(1-sinx)y=log cosx - log (1-sinx)dy/dx= -sinx/cosx + cosx/ 1-sinxdy/dx= -tanx + cosx(1+sinx)/(1-sinx)(1+sinx)dy/dx= -tanx + 1+sinx/cosxdy/dx=- tanx + secx + tanxdy/dx=sec xproved |
|