The value of `(1+cottheta-co s ectheta)(1+tantheta+sectheta)` is equal to

Options

A. 1
B. 2
C. 0
D. `-1`

Answer

b

Explanation

Shotcut method
`=(1+cot theta-co s ectheta)(1+tan theta+sectheta)`
Put, `theta=45^(@)`
`=(1+cot45^(@)-co s ec45^(@))(1+tan45^(@)+sec45^(@))`
`=(1+1-sqrt(2))(1+1+sqrt(2))`
`=(2-sqrt(2))(2+sqrt(2))`
`=[2^(2)-(sqrt(@))^(2))[(a-b)(a+b)=a^(2)`
`-b^(2))] =4-2=2`