1.

फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए|`log tan (x//2)`

Answer» Correct Answer - `cosecx`
माना ` tan ""(x)/(2) =t " "rArr (dt)/(dx) =(1)/(2) sec ^(2) ""(x)/(2)`
तब ` (d)/(dx) (log tan ""(x)/(2)) =(d)/(dt) (log t ) (dt)/(dx) =(d)/(dt) (logt )*(1)/(2) sec ^(2)""(x)/(2)`
` " "=(1)/(t)*( 1)/(2) sec ^(2) ""(x)/(2)=(1)/(2t) sec ^(2) ""(x)/(2) `
` " "= (1)/(2) (cos x//2)/(sin x //2) *(1)/(cos ^(2)x//2) = (1)/(sin x )= cosec x `


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