Question

Show that `sin^2 5^0+sin^2 10^0+sin^2 15^0++sin^2 90^0=9 1/2dot`

Answer 1

`L.H.S.=(sin^2 5^@+sin^2 85^@)+(sin^2 10^@+sin^2 80^@)+...`
`+(sin^2 40^@+sin^2 50^@)+(sin^2 45^@+sin^2 90^@)`
`(sin^2 5^@+sin^2 5^@)+(sin^2 10^@+sin^2 10^@)+...`
`+(sin^2 40^@+sin^2 40^@)+(sin^2 45^@+sin^2 45^@)`
`=(1+1+1+1+1+1+1+1)`
`+(1/sqrt2)^(2)+1=9 1/2=R.H.S.`