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2006-09-10 00:20:58 · 7 answers · asked by frank castle 1 in Science & Mathematics ➔ Mathematics
tan 5x = cot 3x
= tan [pi/2 -3x]
=> 5x = n(pi) + pi/2 -3x
=> 5x+3x = n(pi) + pi/2
=> 8x = 2n(pi/2) +pi/2
=> 8x = (2n+1)pi/2
=> x = (2n+1)pi/16
Hence proved
2006-09-10 01:20:32 · answer #1 · answered by spnchennai 1 · 0⤊ 0⤋
LHS: tan 5x= sin5x/cos5x
RHS: cot 3x = cos3x/sin3x
Bring over sin3x to RHS, cos5x to LHS, then you have:
sin3xsin5x=cos5xcos3x
cos5xcos3x - sin3xsin5x = 0
Using addition formula of cos ( A + B ) = cosAcosB - sinAsinB
cos ( 5x + 3x ) = 0
cos8x=0
General solution for cos X = k where -1
A = cos^-1 ( 0 ) = TT/2
8x = 2n TT + TT/2
8x= ( TT ( 4n + 1))/2
x = (4n + 1)pi/16
or x = ( 4n -1)pi/16
2006-09-10 00:38:30 · answer #2 · answered by lkraie 5 · 0⤊ 0⤋
A more simple way.
tan 5x = cot 3x
tan 5x = tan (pi/2 -3x)
=> 5x=k(pi) + (pi/2 - 3x)
=> 8x=k(pi) + pi/2
=> x=k(pi/8) + pi/16
2006-09-10 00:50:39 · answer #3 · answered by Babax 3 · 0⤊ 0⤋
Substitute the value of x and then try to solve. The problem is meaningless wthout the value of n. so you'll have to know that. Did you make this on your own??! coz pi/16 = 11.25!!
2006-09-10 00:27:25 · answer #4 · answered by Lady_Marmalade 2 · 0⤊ 0⤋
2n+1 = 3 equals cot, dont know anything else im to dumb!!~!
2006-09-10 00:22:43 · answer #5 · answered by jobe j 2 · 0⤊ 0⤋
what type of math is this? calculus and algebra follow different rules. It's been over a year since I've done problems like this...
2006-09-10 00:26:44 · answer #6 · answered by Workin Hard 1 · 0⤊ 0⤋
dont know
2006-09-10 00:22:58 · answer #7 · answered by ms 1 · 0⤊ 0⤋