Question

5. If theta is the angle x/a+y/b=1and x/b+y/a=1 find the value of sin theta when a>b
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Answer 1

Answer: sin θ = a^2 - b^2 / a^2 + b^2

Step-by-step explanation:

I am assuming that the question is "If θ is the angle between the lines

x/a + y/b = 1, x/b + y/a = 1, then cosθ =?"

For line 1, the equation is y = (- b/a)x + b and for line y = (-a/b)x + a.

So the slopes are: m1 = -b/a , m2 = -a/b.

tan θ = | m2 − m1 / 1 + m1 m2 |

        = a^2 - b^2 / 2ab

tan θ = opposite / adjacent side in a triangle.

Hypotenuse is [ (a^2 - b^2)^2 + 4a^2b^2] ^ 1/2 = a^2 + b^2

So sin θ = opposite / hypotenuse

sin θ = a^2 - b^2 / a^2 + b^2