The value of ((1-cotθ)/(1-tanθ))² +1, if 0° < θ < 90°, is equal to:

The value of ((1-cotθ)/(1-tanθ))² +1, if 0° < θ < 90°, is…

The value of $(\frac{1-cotθ}{1-tanθ})^2$ +1, if 0° < θ < 90°, is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. cosec²θ

1 - cotθ = (tanθ - 1)/tanθ

⇒ $(\frac{1-cotθ}{1-tanθ})$ = -1/tanθ

$(\frac{1-cotθ}{1-tanθ})^2$ = 1/tan²θ

And, 1/tan²θ = cot²θ

So, cot²θ + 1 = cosec²θ