Question

Please help me with this question

Answer 1

cos(x-30)=1/2

Explanation:

We use the following relationship to obtain cos(x)

`sin^(2)(x) +cos^(2)(x) +1`

From that, we have that cos(x)= sqrt(1-1/4)=sqrt(3) / 4

To obtain the value of cos(x-30), lets remember the following expression:

`cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)`

Therefor, we can use that to obtain our desired function cos(x-30)

cos(x)*cos(30)+sin(x)*sin(30)

`(√(3) )/(2) * (√(3) )/(2)  +(-1)/(2)*(1)/(2)`

=2/4=1/2