NDA2017MathematicsInverse Trigonometric FunctionsActual
Let x , y , z be positive real numbers such that x , y , z are in GP and ⁻¹ x, ⁻¹ y and ⁻¹ z are in AP. Then which one of the following is correct?
Options
- Ax = y = z
- Bxz =1
- Cx y and y=z
- Dx=y and y z
Correct answer
A. x = y = z
Step-by-step solution
aligned & 2 ⁻¹ y= ⁻¹ x+ ⁻¹ z & ( ⁻¹, ⁻¹ y, ⁻¹ z are in A.P ) & and x, y, z are in G.P y^2=x z...(i) aligned aligned & 2 y 1-y^2 = x+z 1-x z & 2 y 1-y^2 = x+z 1-y^2 & 2 y=x+z & x, y, z are in A.P. aligned (from (i)) Given x, y, z are also in G.P So, x=y=z