Question

Let $α$ and $β$ be such that $α+β=π$.If $cosα=\dfrac{1}{√2}$ ,then the value of $cot (β-α)$ is

• A. $∞$
• B. $\dfrac{1}{2}$
• C. $\dfrac{1}{4}$
• D. $1$
• E. $0$
• F. Undefined

Answer 1

Answer: (F)

Undefined

Answer 2

Given that:

Let $α$ and $β$ be such that: $α+β=π$.

$cosα=\dfrac{1}{√2}$,

we need to find the value of $cot(β - α),$

So we know that,

$cot(β - α) = cot(π - (α + β))$

⇒ $cot(β - α) = cot(π - π)$ (⇢ $α + β = π$,)

⇒ $cot(β - α)= cot(0)$

⇒$cot(β - α)= \text{undefined}$

Hence , answer is not infinity rather undefined.