Question

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

• A. 1
• B. 2
• C. -1

Answer 1

The correct option is B 2

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