If `theta=3alpha` and `sin theta=(a)/(sqrt(a^(2)+b^(2))` , the value of the expression `a co sec alpha-b sec alpha` is

Options

A. `(a)/(sqrt(a^(2)+b^(2))`
B. `2sqrt(a^(2)+b^(2))`
C. a+b
D. none of these.

Answer

B

Explanation

`(sqrt(a^(2)+b^(2)))/(sin alpha cos alpha)[(a)/(sqrt(a^(2)+b^(2)))cosalpha-(b)/sqrt(a^(2)+b^(2))sinalpha]``(sqrt(a^(2)+b^(2)))/(sin alpha cos alpha)[(a)/(sqrt(a^(2)+b^(2)))cosalpha-(b)/sqrt(a^(2)+b^(2))sinalpha]`` (sqrt(a^(2)+b^(2)))/(sin alpha cos alpha)[(a)/(sqrt(a^(2)+b^(2)))cosalpha-(b)/sqrt(a^(2)+b^(2))sinalpha]`
Now, `sin3 alpha=(a)/sqrt(a^(2)+b^(2))` gives
`sqrt(a^(2)+b^(2))` `[(sin3alphacos alpha-cos 3alpha sin alpha)/(sin alpha cos alpha)]=2sqrt(a^(2)+b^(2))`