Simplify: `(1+tan^(2)theta)(1-sintheta)(1+sintheta)`

Options

A. `0`
B. `1`
C. `2`
D. `3`

Answer

B

Explanation

`(1+tan^(2)theta)(1-sintheta)(1+sintheta)= (1+tan^(2)theta)(1-sin^(2)theta)` `[therefore (a-b)(a+b)=a^(2)-b^(2)]`
`=sec^(2)theta. Cos^(2)theta` `[therefore 1+tan^(2)theta= sec^(2)theta` and `cos^(2)theta + sin^(2)theta=1]`
`=1/(cos^(2)theta).cos^(2)theta=1` `[therefore sectheta=1/(costheta)]`