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If sin(a + b) = 3/4 and sin(a - b) = 1/2, then find tan(a)/tan(b).

 May 24, 2020
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sin(a+b) = sinacosb +cosasinb = 3/4       (1)

sin(a-b) =  sinacosb -cosasinb = 1/2      (2)        or   - sinacosb+cosasinb= -1/2      (3)

 

  add (1) and (2) together:   2 sina cosb = 5/4     re-arrange  sina cosb = 5/8     (4)

  add  (1) and (3) together   2 cosasinb = 1/4      rearrange   cosa sinb =  1/8     (5)

 

tana /tanb  =   sina/cosa  /  sinb/cosb 

                  = sina  cosb    /   cosa sinb      sub in  (4) and (5)

                          =   5/8    /   1/8     = 5

 May 24, 2020

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