The value of `sin^3 10^0+sin^3 50^0-sin^3 70^0` is equal to `-3/2` (b) `3/4` (c) `-3/4` (d) `-3/8`

Options

A. `-(3)/(2)`
B. `(3)/(4)`
C. `-(3)/(4)`
D. `-(3)/(8)`

Answer

D

Explanation

We have `sin^(3)10^(@)+sin^(3)50^(@)-sin^(3)70^(@)`
`=(1)/(4)[(3sin10^(@)-sin30^(@))+(3sin50^(@)-sin150^(@))-(3sin70^(@)-sin210^(@))]`
`=(1)/(4)[3(sin10^(@)+sin50^(@)-sin70^(@))-(3)/(2)]`
`=(1)/(4)[3(sin 10^(@)-2cos60^(@).sin10^(@))-(3)/(2)]=-(3)/(8)`