Let `x=sin1^@` then find the value of the expression `1/(cos0^@cos1^@)+1/(cos1^@cos2^@)+....+1/(cos44^@cos45^@)`

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)`