can you simplify this trig problem, and just tell me what you got... i already did it, and i got the Square root of 3, but i think the answer should be neg... any ways, help please...
the identiy used is tan2x = (2tanx) / (1-tan^2 x )
here is the prob..
verify the identity for..
tan 2x when x = Pi/3
so any hep please.. .thanx
2007-11-07 14:27:41 · 5 answers · asked by john doe 2 in Science & Mathematics ➔ Mathematics
x = π/3
tan(x) = √3
tan²(x) = (√3)² = 3
tan(2x) = 2tan(x) / (1-tan²(x))
= 2*√3 / (1 - 3)
= 2*√3 / (-2)
= -√3
2007-11-07 14:34:42 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
LHS
tan(2x) = tan(2pi/3) = tan(pi -pi/3)
=> - tan(pi/3) = -sqrt(3)( in second quadrant tan is negative)
RHS
2tanx/(1-tan^2(x) = 2tan(pi/3)/(1- tan^2(pi/3)
=>2sqrt(3)/(1- 3) = 2sqrt(3)/-2 = - sqrt(3)
LHS = RHS
2007-11-07 14:41:31 · answer #2 · answered by mohanrao d 7 · 0⤊ 0⤋
you are right, it should be -sqrt(3)
tan(pi/3) = sqrt(3)
2tanx/(1-tan^2x)= 2sqrt(3)/(1- sqrt(3)^2)
= 2 sqrt(3)/(1-3) = 2 sqrt(3)/-2 = -sqrt(3)
angle 2pi/3 is in the second quad and tan is negative.
2007-11-07 14:35:20 · answer #3 · answered by norman 7 · 0⤊ 0⤋
Did you check you computation on the denominator...it is 1-(tan(pi/3)^2 and not (-tan(pi/3))^2.
2007-11-07 14:36:08 · answer #4 · answered by ted s 7 · 0⤊ 1⤋
you're able to rewrite your equations. (csc0 - a million) implies (csc(0) - a million), yet i'm uncertain if that's what you recommend. additionally, please use x rather of 0, or flow replica the theta image from Wikipedia.
2016-09-28 13:46:57 · answer #5 · answered by ? 4 · 0⤊ 0⤋