Question

Solve $(1+\tan \theta +\sec \theta )(1+\cot \theta -\csc \theta )$

• A. $0$
• B. $2$
• C. $1$
• D. $-1$

Answer 1

Answer: (B)

$2$

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

According to question,

Convert given eq. into $sine,cosine$, We get,

$=(1+\frac{sin\theta }{cos\theta }+\frac{1}{cos\theta })(1+\frac{cos\theta }{sin\theta }-\frac{1}{sin\theta })$

$=\left(\frac{cos\theta +sin\theta +1}{cos\theta }\right)\left(\frac{cos\theta +sin\theta -1}{sin\theta }\right)$

$=\frac{(cos\theta +sin\theta {)}^2-1^2}{cos\theta sin\theta }$

(1+tanθ+secθ)(1+cotθ−\cos ecθ)

$=\frac{1+2sin\theta cos\theta -1}{cos\theta sin\theta }$

$=\frac{2sin\theta cos\theta }{cos\theta sin\theta }$

$=2$