Here 'alpha' is denoted by '@'.
2006-08-14 17:53:10 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Show that x=npie+@/2 or (2n+1)pie/6 - @/6
2006-08-14 20:35:19 · update #1
sin@/sin2x + cos@/cos2x = 2
Multiply both sides by sin2x * cos2x to get
sin@cos2x + cos@sin2x =2(sin2x*cos2x)
Apply the identity sin2A = 2sinA*cosA to the right side to get
sin@cos2x + cos@sin2x = sin4x
Apply the identity sin(A+B) = sinAcosB +cosAsinB to the left side:
sin(@+2x) = sin4x
Therefore @+2x = 4x; @ = 2x so
x = @/2
2006-08-14 20:22:57 · answer #1 · answered by gp4rts 7 · 0⤊ 0⤋
@=2
2006-08-14 17:59:41 · answer #2 · answered by rich-k 2 · 0⤊ 0⤋
The answer is 2 like the number of points for answering this.
2006-08-14 17:58:30 · answer #3 · answered by Ron D 4 · 0⤊ 0⤋
I think it is x = @/2
I had to add the fractions, then do a trig ID on the numerator:
sin(2x + @) = 2*sin(2x)cos(2x)
Then another ID
sin(2x + @) = sin(4x)
Take the arcsin, and solve
2x + @ = 4x
2006-08-14 18:00:43 · answer #4 · answered by Captain_Ahab_ 3 · 0⤊ 0⤋