Let `x=sin1^0,` then the value of the expression. `1/(cos0^0dotcos1^0)+1/(cos1^0dotcos2^0)+1/(cos2^0dotcos3^0)+1/(cos44^0dotcos45^0)` is equal to `x` (b) `1/x` (c) `(sqrt(2))/x` (d) `x/(sqrt(2))`

Options

A. x
B. `1//x`
C. `sqrt(2)//x`
D. `x//sqrt(2)`

Answer

B

Explanation

`(1)/(sin1^(@))[(sin(1^(@)-0^(@)))/(cos 0^(@)cos1^(@))+(sin(2^(@)-1^(@)))/(cos1^(@)cos2^(@))+(sin(3^(@)-2^(@)))/(cos2^(@)cos3^(@))+............+(sin(45^(@)-44^(@)))/(cos44^(@)cos45^(@))]`
`(1)/(sin1^(@))[tan1^(@)+(tan2^(@)-tan1^(@))+(tan3^(@)-tan2^(@))+(tan4^(@)-tan3^(@))+........+(tan45^(@)-tan44^(@))]`
`=(1)/(sin1^(@))=(1)/(x)`