Question

If thita is the angle between the lines x/a +y/b=1 And x/b+y/a=1 then find the value of sin theta

Answer 1

Answer:

The value of sinθ = (a² - b²)/(a² + b²)

Step-by-step explanation:

For line ,  x/a +y/b=1

slope of the line, m₁ = -b/a

For line, x/b+y/a=1

slope of the line , m₂ = -a/b

If θ is the angle between them, then

tanθ = (m₁ - m₂)/(1 + m₁m₂)

=> tanθ = (-b/a + a/b)/ (1 + 1)

=> tanθ = (a² - b²)/2ab

since tanθ = p/b , then sinθ = p/h = p/√p²+b²

Here,

p = (a² - b²)

b = 2ab

=> h = √(a² - b²)² + (2ab)²

= √( a⁴ + b⁴ -2a²b² + 4 a²b²)

= √(a⁴  + b⁴ + 2a²b² )

= √(a² + b²)²

= (a² + b²)

sinθ = (a² - b²)/(a² + b²)

which is the required value.

Answer 2

Step-by-step explanation:

sin theta= a^2 -b^2/a^2 +b^2