If cosθ = 1213, then the value of ( 1 - ) ( 1 + cosec ) is:

Answer: Option B

$$\begin{array}{rl}& \cos \theta =\frac{12}{13}=\frac{B}{H}\\ & P=\sqrt{{13}^2-{12}^2}=5\text{cm}\\ & \frac{\sin \theta \left(1-\tan \theta \right)}{\tan \theta \left(1+\text{cosec}\theta \right)}\\ & =\frac{\frac{P}{H}\left(1-\frac{P}{B}\right)}{\frac{P}{B}\left(1+\frac{H}{P}\right)}\\ & =\frac{\frac{5}{13}\left(1-\frac{5}{12}\right)}{\frac{5}{12}\left(1+\frac{13}{5}\right)}\\ & =\frac{\frac{5}{13}\times \frac{7}{12}}{\frac{5}{12}\times \frac{18}{5}}\\ & =\frac{\frac{35}{156}}{\frac{3}{2}}\\ & =\frac{35\times 2}{156\times 3}\\ & =\frac{35}{234}\end{array}$$