when two vectors A and B inclined at an angle theta act on a body, the resultant is (2k-1)under root(A^{2_{+B2).when the vectors are inclined at an angle (90-theta),the resultant is(2k-1)under root A2+B2,thenprove that.............tan (theta)=k-1/k+1}}

As we know resultant vector can be given as:

R ² = A ² + B ² + 2AB cosθ  -----------(1)

Now as given, R = (2k-1) (A² + B²)^1/2 ---------------------(2)  

Comparing both equations:

(2k-1)² (A² + B²) = A² + B ²+ 2AB cosθ  

(4k² + 1 -4k) (A² + B²) = A² + B ²+ 2AB cosθ 

Proceeding the calculation further we can get the value of the inclination angle.