फलन `f : (-1,1) to R` इस प्रकार है कि `f (cos 4 theta) = (2)/(2 –sec^(2) theta)`जहाँ `theta epsilon (0,(pi)/(4)) uu ((pi)/(4),(pi)/(2))` तब ` f ((1)/(3))` का मान क्या होगा।

Explanation

`:. , , f (cos 4 theta) = (2)/(2-sec^(2) theta)`
`cos 4 theta =(1)/(3) ` रखने पर
`cos 2 xx 2theta = (1)/(3)`
`2 cos^(2) 2 theta -1 =(1)/(3)`
`2 cos^(2) 2theta =1 +(1)/(3)`
`2 cos^(2) 2theta = (4)/(3)`
`cos^(2) 2 theta =(2)/(3)`
` cos 2theta = -+ sqrt((2)/(3))`
समीकरण (i) से
` f (cos 4 theta) = (2)/(2-(1)/(cos^(2) theta)) = (2 cos^(2) theta)/(2 cos^(2) theta-1) = (1+ cos 2 theta)/(cos 2 theta) = (1+(+-sqrt((2)/(3))))/((+- sqrt((2)/(3))))`