Question

if
$cot a + \frac{1}{cot \: a} = 1$
then
$cota ^{2} + \frac{1}{cot {}^{2} } = ?$

answer please​

Answer 1

Answer:

-1

Step-by-step explanation:

Given that cot a + 1/cot a = 1 then what will be the value of cot²a + 1/cot²a

To find the value of cot²a + 1/cot²a. Do squaring on both sides of cot a + 1/cot a = 1

So, let's start by squaring it,

→ (cot a + 1/cot a)² = (1)²

Now,

Used identity: (a + b)² = a² + b² + 2ab

→ (cot a)² + (1/cot a )² + 2 × cot a × 1/cot a = 1

→ cot² a + 1/(cot² a) + 2 = 1

→ cot² a + 1/(cot² a) = 1 - 2

→ cot² a + 1/(cot² a) = - 1

Hence, the value of cot² a + 1/(cot² a) is -1.