1.

(i ) यदि `y= log sqrt(((1+ sin x )/(1-sin x ))),` तब ` (dy)/(dx)` ज्ञात कीजिए (ii) यदि ` y= log sqrt(((1-cos x)/(1+cos x ))), `तब `(dy)/(dx)` ज्ञात कीजिये|

Answer» Correct Answer - `(i) secx " "(ii) cosecx`
(i ) माना ` sqrt((1+sin x )/(1-sinx ))= t" "rArr " "(1)/(2) log ((1+sin x )/(1-sin x ))=log t `
` rArr " "[ (1)/(2) (1)/(((1+sin x)/(1-sinx)))*(d)/(dx) ((1+ sin x )/(1-sinx ))]dx =(1)/(t) dt `
` rArr (1)/(t)(dt)/(dx) =((1-sinx ))/(2(1+sin x ) ) ((1-sinx ) (d)/(dx) (1+ sinx ) -(1+sinx )(d)/(dx) (1- sin x ))/((1-sin x)^(2))`
सरल करने के बाद `(dt)/(dx) =sqrt((1+sin x)/(1-sinx ))sec x`
तब ` " "(dy)/(dx) =(d)/(dt) (logt ) (dt)/(dx) ` का प्रयोग करने पर


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