12 sin x/2 sin 3x/2 = 2cos 5x/2 sin 3x/2
=> sin x/2 = cos 5x/2
=> cos ( pi/2 - x/2 ) = cos 5x/2 +> x= pi /6
=.> cos 3x - sin 3x = -1
plz correct me if i m wrong
FIND cos(3x) - sin(3x)
IF cos(2x) - cosx = sin(4x) - sinx
AND tanx is not 1!!!
-
UP 0 DOWN 0 0 6
6 Answers
29dunno how it came to my mind...sharp observation i guess ..put x = π/2..and u will get the answer..btw trying for the actual solution..will post it in a while...
1
1write sin4x as sin(3x+x) and cos2x as cos(3x-x) then use the formula of sin(a+b) and cos(a-b)
1From the equation cos 2x - cos x = sin 4x - sin x
we get ---- - 2 { sin 3x / 2 } { sin x / 2 } = 2 { sin x / 2 } { cos 5x / 2 }
so , sin 3x /2 = - cos 5x / 2 = sin ( 5x / 2 - pi / 2 )
so 3x / 2 = 5x / 2 - pi / 2
or , x = pi / 2
Hence cos 3x = 0
Sin 3x = - 1
Hence the answer should be 1 .
49oh my god gallardo!! how can you be such a genius!!KUDOS to you!!
btw are u a student???[3][3][3][3]
24cos(2x) - cosx = sin(4x) - sinx
holds for x=0 as well...
and ans that way too is 1