Question

If cot A = `5/12` the value of cot² A × cosec² A is ______.

Options

• 1

• 2

• −2

• −1

Answer 1

If cot A = `5/12` the value of cot² A × cosec² A is −1.

Explanation:

Using the trigonometric identity csc² A − cot² A = 1, we can rearrange it to find cot² A − csc² A = −1. Alternatively, substituting \[\cot A = \frac{5}{12}\] gives \[\cot^2 A = \frac{25}{144}\] and \[\csc^2 A = 1 + \cot^2 A = \frac{169}{144}\], resulting in \[\frac{25}{144} - \frac{169}{144} = -1\].