If x=acosθ and y=bcotθ ,then (ax^-1-by^-1)(ax^-1+by^-1) is equal to 

Consider the followng statements

1.(1+tan²θ)/(1+cot²θ)=[(1-tanθ)/(1-cotθ)]² is true for all 0<θ<π/2,θ≠π/4

2.cotθ=1/tanθ is true for θ=45° only

Which of the above statement is/are correct?

20% of a number when added to 20 becomes the  number itself,then the number is

Which one of the following is correct? 

The sum of first 47 terms of the series (1/4+1/5-1/6-1/4-1/5+1/6+1/4+1/5-1/6... is

Three athletes run a 4km race.Their speeds are in the ratio 16:15:11.When the winner wins the race,distance between the athlete in the second position to the athlete in the third position is