Question

Can you please help me out is it A- trueB- False

Answer 1

According to the trigonometric properties, we have the following

1.

`\sin (x+y)=\sin x\cdot\cos y+\cos x\cdot\sin y`

2.

`\cos (x-y)=\cos x\cdot\cos y+\sin x\cdot\sin y`

we replace the above into the right hand side of the equation

`(1)/(2)((\sin x\cdot\cos y+\cos x\cdot\sin y)\cdot(\cos x\cdot\cos y+\sin x\cdot\sin y))`

1/2now, let's continue expanding the above

`(1)/(2)((\sin x\cdot\cos y\cdot\cos x\cdot\cos y)+(\sin x\cdot\cos y\cdot\sin x\cdot\sin y)+(\cos x\cdot\sin y\cdot\cos x\cdot\cos y)+(\cos x\cdot\sin y\cdot\sin x\cdot\sin y))`

if we simplify this, we will obtain

`=(1)/(2)\cos \mleft(x-y\mright)\sin \mleft(x+y\mright)`

on the other hand,

From the trigonometric property sinx * cosy, this is the same as

`\sin x\cdot\cos y=(1)/(2)((\sin x-y)+\sin (x+y))`

Therefore, the statement must be false