Simplify: \frac{\sin(3x-y)-\sin(3y-x)}{\cos(2x)+\cos(2y)} I used the formula: \sin(\alpha)-\sin(\beta)=2*\cos... and got to: \frac{\sin(2x-2y)}{\cos(x-y)}

Kymani Shepherd

Kymani Shepherd

Answered question

2022-04-26

Simplify: sin(3xy)sin(3yx)cos(2x)+cos(2y)
I used the formula:
sin(α)sin(β)=2cos
and got to:
sin(2x2y)cos(xy)

Answer & Explanation

wellnesshaus4n4

wellnesshaus4n4

Beginner2022-04-27Added 24 answers

After getting
sin2x-2ycosx-y
Which is
sin2x-ycosx-y
Using Double Angle Formula,
sin2θ=2·cosθsinθ
We get our expression as,
2·sinx-ycosx-ycosx-y
And we are left with
2sinx-y

ritmesysv

ritmesysv

Beginner2022-04-28Added 12 answers

Note that sin(2x2y)=sin(2(xy))=2sin(xy)cos(xy), so
sin(2x2y)cos(xy)=2sin(xy)cos(xy)cos(xy)=2sin(xy)
Of course with the exception of when cos(xy)=0

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