Question

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to

Options

• 0

• 1

•  −1

• None of these

Answer 1

None of these 

`(cosec ecθ-sinθ)(secθ-cos θ)(tan θ+cot θ)` Simplifying the given expression, we have 

`(cosec θ-sinθ)(secθ-cosθ)(tanθ+cot θ)`

`=(1/sinθ-sinθ)(1/cos^2 θ-cosθ)(sin θ/cos θ+cos θ/sinθ)`

`=1-sin^2θ/sinθ xx(1-cos^2θ)/cos θ xx (sin^2θ+cos^2θ)/(sin θ cos θ)` 

=` cos^2θ/sin θ xx sin^2θ/cosθxx1/(sinθ cosθ)` 

=`(cos^2θ sin^2θ)/(sin^2θ cos^2θ)`

= `1`