Question

(sec² θ – 1) (cosec² θ – 1) is equal to ______.

Options

• –1

• 1

• 0

• 2

Answer 1

(sec² θ – 1) (cosec² θ – 1) is equal to 1.

Explanation:

(sec² θ – 1) (cosec² θ – 1) = tan² θ.cot² θ  ...`[(∵ sec^2 θ - 1 = tan^2 θ),("cosec"^2 θ - 1 = cot^2 θ)]`

= `tan^2 θ . 1/tan^2 θ`  

= 1