Question

Cos^2x+cos^2(120°+x)+cos^2(120°-x)
i need this asap. pls help me​

Answer 1

`(3)/(2)`

Explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= -
`(1)/(2)` cosx -
`(√(3) )/(2)` sinx

squaring to obtain cos² (120 + x)

=
`(1)/(4)`cos²x +
`(√(3) )/(2)`sinxcosx +
`(3)/(4)`sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= -
`(1)/(2)`cosx +
`(√(3) )/(2)`sinx

squaring to obtain cos²(120 - x)

=
`(1)/(4)`cos²x -
`(√(3) )/(2)`sinxcosx +
`(3)/(4)`sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x +
`(1)/(4)`cos²x +
`(√(3) )/(2)`sinxcosx +
`(3)/(4)`sin²x +
`(1)/(4)`cos²x -
`(√(3) )/(2)`sinxcosx +
`(3)/(4)`sin²x

= cos²x +
`(1)/(2)`cos²x +
`(3)/(2)`sin²x

=
`(3)/(2)`cos²x +
`(3)/(2)`sin²x

=
`(3)/(2)`(cos²x + sin²x) =
`(3)/(2)`