What is the value of (tanƟ cosecƟ)2 -(sinƟ secƟ)2

What is the value of (tanƟ cosecƟ)2 -(sinƟ secƟ)2

Options:

A. -1
B. 0
C. 1
D. 2

Correct answer is option C.

1. Explanation: = `("tanƟcosecƟ")^2` - `("sinƟsecƟ")^2`

= `"tan"^2Ɵ` `"cosec"^2Ɵ` - `"sin"^2Ɵ` `"sec"^2Ɵ`

= `\frac{"sin"^2 Ɵ}{"cos" ^2Ɵ} \times \frac{1}{"sin"^2 Ɵ} - "sin"^2 Ɵ \times \frac{1}{"cos"^2Ɵ }`

= `\frac{1- "sin"^2Ɵ}{"cos"^2Ɵ}`

= `\frac{"cos"^2Ɵ}{"cos"^2Ɵ}` = 1

Thus , the value of (tanƟ cosecƟ)2 -(sinƟ secƟ)2 is 1.