Question

Which numbers complete the blanks when solving the equation Cosine (x + 2 pi) = negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction over the interval [0, 2Pi]?

Cosine x times blank minus sine x times blank = negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction

Answer 1

A. 1;0

Explanation:

did on edge

Answer 2

Thus, the blanks should be completed with 1;0 respectively

Explanation:

Cosine of the sum of angles

The formula for the cosine of angles \alpha and \beta is shown below:

`cos(\alpha+\beta)=cos\alpha*cos\beta-sin\alpha*sin\beta`

For the expression given in the question:

`cos(x+2\pi)=cosx*cos2\pi-sinx*sin2\pi`

Since

`cos 2\pi=1, sin2\pi=0:`

`cos(x+2\pi)=cosx*1-sinx*0`

Thus, the blanks should be completed with 1;0 respectively