# Compound Angle Formula

#### coolhacker

Hi everyone!

plz help me solve this Compound Angle Formula question:

1. Using Compound Angle Formula, prove that:

cos(y - 180°) + sin (y +
90°) = 0

plz thxx
(Clapping)(Talking)

#### harish21

Hi everyone!

plz help me solve this Compound Angle Formula question:

1. Using Compound Angle Formula, prove that:

cos(y - 180°) + sin (y +
90°) = 0

plz thxx
(Clapping)(Talking)
$$\displaystyle cos(A-B) = (cosA \times cosB) + (sinA \times sinB)$$

$$\displaystyle sin(A+B) = (sinA \times cosB) + (cosA \times sinB)$$

coolhacker

#### Soroban

MHF Hall of Honor
Hello, coolhacker!

We are expected to know these formulas:

. . $$\displaystyle \cos(A-b) \;=\;\cos A\cos B + \sin A\sin B$$

. . $$\displaystyle \sin(A + B) \;=\;\sin A\cos B + \cos A\sin B$$

1. Using Compound Angle Formulas, prove that:

. . . . . $$\displaystyle \cos(y - 180^o) + \sin (y + 90^o) \;=\;0$$

We have: . $$\displaystyle \cos(y-180^o) \qquad\quad+ \quad\qquad\sin(y+90^o)$$

. . $$\displaystyle =\;\;\overbrace{\cos y \cos180^o + \sin y \sin180^o} + \overbrace{\sin y\cos90^o + \cos y\sin90^o}$$

. . $$\displaystyle =\;\;\;\cos y\,(-1) \quad+\quad \sin y\,(0) \quad+\quad \sin y\,(0) \quad+ \quad \cos y\,(1)$$

. . $$\displaystyle =\qquad -\cos y \qquad + \qquad 0 \qquad + \qquad 0 \qquad + \qquad \cos y$$

. . $$\displaystyle =$$ . . . . . . . . . . . . . . . . . .$$\displaystyle 0$$

thx u