If x, y and z are the sides of a right angled triangle, where ‘z’ is the…
2023
If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of (1/logx+zy) + (1/logx-zy)
- A.
1
- B.
2
- C.
3
- D.
4
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Key identity: 1/log_a b = log_b a
Apply the identity to each term: 1/log_{x+z} y = log_y(x+z) and 1/log_{z-x} y = log_y(z-x).
Add the two logarithms: log_y(x+z) + log_y(z-x) = log_y[(x+z)(z-x)].
Simplify the product: (x+z)(z-x) = z^2 - x^2, so the expression becomes log_y(z^2 - x^2).
Use the Pythagorean relation (since z is the hypotenuse): z^2 = x^2 + y^2, hence z^2 - x^2 = y^2.
Therefore the value is log_y(y^2) = 2.
Answer: 2