` sin ^(2) 5^(@) + sin^(2) 10^(@) + sin^(2) 15^(@) + sin ^(2) 20^(@) + . . . + sin ^(2) 90^(@) ` मान क्या है ?

Options

A. `7`
B. `8`
C. `9`
D. `19/2`

Answer

D

Explanation

` sin ^(2) 5^(@) + sin^(2) 10^(@) + sin ^(2) 15^(@)`
` + . . . +sin^(2) 90^(@)`
` = (sin^(2) 5^(@) + sin^(2) 85^(@))`
` + (sin^(2)10^(@) +sin^(2) 80^(@))+. . . `
` = sin^(2) 45^(@) + . . . + sin^(2) 90^(@)`
` = sin^(2) 5^(@) + sin^(2) (90^(@)- 5^(@)) + sin^(2) 10^(@) `
` = sin^(2) 5^(@) +sin^(2) (90^(@)- 10^(@)) +. . . + sin^(2) 90^(@) `
` + ( sin^(2) 10^(@) +cos^(2) 10^(@))+. . . +sin^(2) 90^(@)`
` 1 + 1+ 1+ 1 + 1+1 +1 `
` +1+ (1/sqrt(2))^(2)+1`
` = 9 + 1/2 = 19/2 `