Find the value of : `sin^2(pi/(18))+sin^2(pi/9)+sin^2((7pi)/(18))+sin^2((4pi)/9)`

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

`L.H.S. = sin^2(pi/18)+sin^2((pi)/9)+sin^2((7pi)/18)+sin^2((4pi)/9)`

`=sin^2 10^@+ sin^2 20^@+ sin^2 70^@+sin^2 80^@`

`=sin^2 10^@+ sin^2 80^@+ sin^2 70^@+sin^2 20^@`

`=sin^2 10^@+ sin^2 (90-10)^@+ sin^2 (90-20)^@+sin^2 20^@`

`=(sin^2 10^@+ cos^2 10^@)+ (cos^2 20^@+sin^2 20^@)`

`=1+1= 2 = R.H.S.`