Question

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) =
A. 0
B. 1
C. 1
D. −1

Answer 1

Answer:

Answer is option A zero.

Answer 2

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = 2

Step-by-step explanation:

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = (1 + sinθ / cosθ + 1/cosθ) (1 + cosθ /sinθ  -1/sinθ)

=  [(cosθ + sinθ + 1)/ cosθ] [(sinθ + cosθ -1)/sinθ ]

= [(cosθ + sinθ)² - 1²] / cosθsinθ

= (cos²θ + sin²θ + 2cosθsinθ - 1)/ cosθsinθ

= 2cosθsinθ + 1 - 1 / cosθsinθ  

= 2cosθsinθ / cosθsinθ  

= 2

2 is the answer and it is not given in the options.