Question 54

What is the value of

$$ \left\{ \sin (90 + x) \cos [\pi - (x - y)] \right\}$$ $$+ \left\{ \cos (90 + x) \sin [\pi - (x - y)] \right\}$$?

Solution

We know that : $$Sin\left(A+B\right)=SinACosB+CosASinB\ .$$

So, $$\left\{ \sin (90 +x) \cos [\pi - (x - y)] \right\}$$ $$+ \left\{ \cos (90 + x) \sin [\pi - (x - y)] \right\}$$

$$=Sin\left(\left(90^{\circ\ }+x\right)+\pi\ -\left(x-y\right)\right)\ .$$

$$=Sin\left(90^{\circ\ }+x+180^{\circ\ }-x+y\right)\ .$$

$$=Sin\left(270^{\circ\ }+y\right)\ .$$

$$=-Cos\ y\ .$$

A is correct choice.

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