Question

Prove that
secθ+1 / tanθ = tanθ / secθ−1

Answer 1

To prove that secθ + 1 / tanθ = tanθ / secθ−1, we can use trigonometric identities.

First, we will define secθ as 1/cosθ and tanθ as sinθ/cosθ.

Now, we can substitute these definitions into the equation to get:

secθ + 1 / tanθ = (1/cosθ) + 1 / (sinθ/cosθ)

And, tanθ / secθ−1 = (sinθ/cosθ) / (1/cosθ) - 1

Expanding both sides using basic algebraic manipulations, we get:

(1/cosθ) + 1 / (sinθ/cosθ) = (1/cosθ) * ((sinθ/cosθ) + cosθ/cosθ)

= (sinθ/cosθ) / (1/cosθ) - 1

= (sinθ/cosθ) * (cosθ/1) - 1

= (sinθ) / 1 - 1

= sinθ.

Therefore, secθ + 1 / tanθ = tanθ / secθ−1 has been proven.