Question

Choose the correct option.
(i) $(1+tan\theta +sec\theta )(1+cot\theta -cosec\theta )$

• A. 1
• B. 2
• C. -1

Answer 1

The correct option is B 2

(C) is correct
$(1+tan\theta +sec\theta )(1+cot\theta -cosec\theta )$
$=(1+sin\theta /cos\theta +1/cos\theta )(1+cos\theta /sin\theta -1/sin\theta )$
$=(cos\theta +sin\theta +1)/cos\theta \times (sin\theta +cos\theta -1)/sin\theta$
$=(cos\theta +sin\theta {)}^2-1^2/(cos\theta sin\theta )$
$=(co{s}^2\theta +si{n}^2\theta +2cos\theta sin\theta -1)/\left(cos\theta sin\theta \right)$
$=(1+2cos\theta sin\theta -1)/\left(cos\theta sin\theta \right)$
$=\left(2cos\theta sin\theta \right)/\left(cos\theta sin\theta \right)=2$