Question

If `cot θ = b/a`, then sec²θ – tan²θ is equal to ______.

Options

• 0

• 1

• –1

• `b/sqrt(a^2 + b^2)`

Answer 1

If `cot θ = b/a`, then sec²θ – tan²θ is equal to 1.

Explanation:

Use the Pythagorean identity sec²θ = 1 + tan²θ. 

So, sec²θ – tan²θ = 1. 

Alternatively, from `cot θ = b/a` ⇒ `tan θ = a/b`.

Then `sec^2θ = 1 + (a^2/b^2)` and sec²θ – tan²θ = 1.