The value of `sin^(2)1+sin^(2)5^(@)+sin^(2)9^(@)+ . . . .+sin^(2)89^(@)` is

Options

A. `11(1)/(2)`
B. `11sqrt(2)`
C. 11
D. `(11)/(sqrt(2))`

Answer

a

Explanation

`sin^(2)1^(@)+sin^(2)5^(@)+sin^(2)9^(@)+....+sin^(2)89`
first identify the number of term:-
1+5+9........89]
Formula:- No. of term
`=("Last term first term")/("difference")+1`
`'N'=(89-1)/(4)+1=22+1=23`
Now `(sin^(2)1^(@)_sin89^(@))+(sin^(2)5^(@)+sin^(2)85^(@))`...........upto 11 pairs+1 middle term
`=11+sin^(2)45rarr` middle term
`=11+(1)/(2)`
`=11(1)/(2)`
Alternate
ह
Ans`=("total no. of term")/(2)=(23)/(2)=11(1)/(2)`
Logic= ह