Question

Tan(x-y) if cscx=13/5 and coty=4/3

Answer 1

Answer:

tan(x-y) = -16/63

Step-by-step explanation

Tan(x-y) if cscx=13/5 and coty=4/3

Given

coty = 4

1/tany = 4/3

Cross multiply

tan y = 3/4

Also since cscx = 13/5

1/sinx = 13/5

sinx = 5/13

Since sinx = opp/hyp

opp = 5

hyp = 13

Get the adjacent

hyp² = opp²+adj²

13² = 5²+adj²

adj² = 13² - 5²

adj² = 169 - 25

adj² = 144

adj = 12

cosx = adj/hyp

cosx = 12/13

tanx = sinx/cosx

tanx = (5/13)/(12/13)

tanx = 5/13 * 13/12

tan x = 5/12

tan(x-y) = tanx - tany/1+tanxtany

tan(x-y) = (5/12 - 3/4)/1+(5/12)(3/4)

tan(x-y) = (5-9/12)/1+5/16

tan(x-y) = -4/12/(21/16)

tan(x-y) = -1/3 * 16/21

tan(x-y) = -16/63