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100 POINTS AND BRAINLIEST!! PRE CALC

Given the sign x = 3/5, sin y = 7/25, and x and y are both acute angles, the value of tan (x - y) is

a. 39/32
b. 44/117
c. 44/7
d. 4/3

Please explain your answer :)

Sagot :

semsee45

Answer:

b. 44/117

Step-by-step explanation:

Calculate tan(x) and tan(y) - can use calculator, or use Pythagoras' Theorem to calculate the length of the 3rd side of the right triangle (as you already have the side opposite to the angle and the hypontenuse, since sin(x) = O/A) and then determine tan(x) using tan(x) = O/A

Then use these values in the tan sum angle trig identity formula.

see attachment for step-by-step

View image semsee45

from both attachments

  • tanx=3/4
  • tany=7/24

Hence

[tex]\\ \rm\Rrightarrow tan(x-y)=\dfrac{tanx-tany}{1+tanx-tany}[/tex]

[tex]\\ \rm\Rrightarrow tan(x-y)=\dfrac{3/4-7/24}{1+(3/4)(7/24)}[/tex]

on solving afterwards

[tex]\\ \rm\Rrightarrow tan(x-y)=\dfrac{11}{24}\times \dfrac{32}{39}[/tex]

[tex]\\ \rm\Rrightarrow tan(x-y)=\dfrac{11}{3}\times \dfrac{4}{39}[/tex]

[tex]\\ \rm\Rrightarrow tan(x-y)=\dfrac{44}{117}[/tex]

Option B

View image Аноним
View image Аноним
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