1.

`int(cosx)/((cos.(x)/(2)+sin.(x)/(2)))` का मान ज्ञात कीजिए।

Answer» दिया है - `I = int (cosx)/((cos.(x)/(2)+sin.(x)/(2)))`
` int (cos^(2)(x//2) -sin^(2)(x//2))/([cos(x//2) +sin(x//2)]^(3))`
` = int(cos (x//2) - sin^(2) (x//2))/([cos(x//2)+sin(x//2))]`
` = int (cos(x//2) - sin(x//2))/((cos.(x)/(2)+sin.(x)/(2)))`
यदि `t= cos.(x)/(2)+sin.(x)/(2)rArr [cos((x)/(2)) -sin((x)/(2))]dx = 2dt`
तब `I = 2int(1)/(t^(2)) dt = -(2)/(t) +c`
` = (-2)/(cos(x//2) +sin(x//2))+c`


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