The expression (tan θ + cot θ ) (sec θ + tan θ ) (1 - sin θ ), 0º θ < 90º, is equal to:

The expression (tan θ + cot θ ) (sec θ + tan θ ) (1 - sin…

The expression (tan $\theta$ + cot $\theta$ ) (sec $\theta$ + tan $\theta$ ) (1 - sin $\theta$ ), 0º < $\theta$ < 90º, is equal to:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. cosec $\theta$ .

(tan $\theta$ + cot $\theta$ ) (sec $\theta$ + tan $\theta$ ) (1 - sin $\theta$ )

(sin $\theta$ /cos $\theta$ + cos $\theta$ /sin $\theta$ ) × (1/cos $\theta$ + sin $\theta$ /cos $\theta$ ) × (1- sin $\theta$ )

(sin² $\theta$ + cos² $\theta$ )/(cos $\theta$ sin $\theta$ ) × (1 + sin $\theta$ )/cos $\theta$ × (1 - sin $\theta$ )

[1/(cos² $\theta$ sin $\theta$ )] × (cos² $\theta$ ) = 1/sin $\theta$

= cosec $\theta$ .