when two vectors A and B inclined at an angle theta act on a body, the resultant is (2k-1)under root(A2+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.

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