(cos(2x)-cos(4x))/(cos(2x)+cos(4x)) how does this fraction turn into (-2sin(3x)sin(-x))/(2cos(3x)cos( can you do a step by step proof to show how the 1st expression turns into the second expression?

Recall the the angle sum identity for cosine.




Adding the two equations together gives



while subtracting gives



Replacing and , you get



Finally, , so you get the second expression.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )