` (cos 15^(@) + cos 45^(@))/(cos^(3) 15^(2) + cos^(3) 45^(@))` का मान क्या है ?

Options

A. `1/4`
B. `1/2`
C. `1/3`
D. इनमे से कोई नहीं

Answer

D

Explanation

`( cos^(@) 15^(@) + cos 45^(@))/(cos^(3) 15^(@) + cos^(3) 45^(@))`
`=(cos 15^(@)+cos 45^(@))/([(cos 15^(@)+cos 45^(@))(cos^(2)45^(@)+cos^(2)15^(@)-cos 45^(@)cos 15^(@))])`
` 1/(( cos^(2) 45^(@) +cos^(2) 15^(@) - cos 45^(@) cos 15^(@)))`
` = 1/(1/2 + ((sqrt((3))+1)/(2sqrt(2)))^(2) - 1/sqrt(2) ((sqrt(3)+1)/(2sqrt(2))))`
` 1/(1/2 +(3+1 +2 sqrt(2))/8 - (sqrt(3)+1)/4)`
` = 1/((4+ 4 + 2 sqrt(3)- 2sqrt(3) -2)/8) = 8/6 = 4/3`