Question

If sin(x-a) = ksin(x+a), express tanx in terms of k and a

Answer 1

Do you know your angle addition and subtracting formulas in terms of sin?

Answer 2

If not check here, then expand it out and rememebr htat tan=sin/cos so maniupulate it their http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 3

Ok, so I could substitute the LHS for cos(a), but then what?

Answer 4

I odnt think just that

Answer 5

ok, I've already expanded the sin functions into sinx cos(a) +- cosx sin(a)

Answer 6

where do I go from there?

Answer 7

Ok can you use the draw tool and type in what you got

Answer 8

ok hold on

Answer 9

\[\sin(x+a) = \sin(x)\cos(a) + \cos(x)\sin(a)\]

Answer 10

\[\sin(x-a) = \sin(x)\cos(a) - \cos(x)\sin(a)\]

Answer 11

ok and the side with addition rmemebr theres a k that has to multiply through

Answer 12

yup

Answer 13

how do i proceed now

Answer 14

Ok i totoally trippeed my se lf up with this, Ill get you some help, nontheless

Answer 15

@satellite73

Answer 16

@uri

Answer 17

now compare both sides:
\[sinxcosa-cosxsina=k(sinxcosa+kcosxsina)\]
\[sinxcosa-cosxsina=ksinxcosa+kcosxsina\]
\[sinxcosa(1-k)=cosxsina(1+k)\]
\[tanx=\frac{ 1+k }{ 1-k }tana\]

Answer 18

omg thank you so much :)