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vitfil [10]
3 years ago
15

The question is in the screenshot

Mathematics
1 answer:
Sidana [21]3 years ago
8 0

Answer:

b. -36/77

Step-by-step explanation:

As 0 < x < \pi/2 => tan x > 0

As 0< y <  \pi/2 => tan y > 0

We have the formula:

  • \frac{1}{sin^{2}x } =1 + cot^{2}x => \frac{1}{(8/17)^{2} } = 1+cot^{2}x => cot^{2} x=225/64

As tan x = 1/(cotx) => tan^{2}x = \frac{1}{cot^{2}x} =\frac{1}{225/64} = \frac{64}{225}

As tan x > 0 => tan x = 8/15

  • \frac{1}{cos^{2}y } = 1+tan^{2}y => \frac{1}{(3/5)^{2} } = 1 + tan^{2} y => tan^{2}y=\frac{16}{9}

As tan y > 0 => tan y = 4/3

As tan (x-y)= \frac{tan x - tan y}{1+ tanx * tany} =\frac{(8/15)-(4/3)}{1+(8/15)*(4/3)} = \frac{-36}{77}  

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