The value of [sin (X + Y) cos (X + Y) + sin (X - Y) cos (X - Y)]/[sin (X + Y) cos (X - Y) + sin (X - Y) cos (X + Y)] is:

The value of [sin (X + Y) cos (X + Y) + sin (X - Y) cos (X - Y)]/[sin (X + Y) cos (X - Y) + sin (X - Y) cos (X + Y)] is: Correct Answer cos 2Y

Given:

Formula Used:

sin 2A = 2 sin A cos A

sin A + sin B = 2 sin (A + B)/2 cos (A - B)/2

sin (A + B) = sin A cos B + cos A sin B

Calculation:

∵ sin 2A = 2 sin A cos A

Numerator = sin (X + Y) cos (X + Y) + sin (X - Y) cos (X - Y)

= ½ sin (2X + 2Y) + ½ sin (2X - 2Y)

= ½        

= ½

= sin 2X cos 2Y

Denominator = sin (X + Y) cos (X - Y) + sin (X - Y) cos (X + Y)

= sin (X + Y + X - Y)

= sin 2X

Hence,

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= (sin 2X cos 2Y)/sin 2X