Find the value of cot x . cot 2 x- cot 2 x . cot 3 x- cot 3 x . cot x.

Question

Find the value of cot x . cot 2 x- cot 2 x . cot 3 x- cot 3 x . cot x. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We know 3 x=2 x +x ⇒ cot 3 x= cot (2 x +x) ⇒ cot 3 x=( cot 2 x ⋅ cot x-1/ cot 2 x+ cot x) ⇒ cot 3 x cot 2 x+ cot 3 x cot x= cot 2 x cot x-1 ⇒ cot x cot 2 x- cot 2 x cot 3 x- cot 3 x cot x=1

Q. Find the value of $cot x . cot 2 x - cot 2 x . cot 3 x - cot 3 x . cot x$ .

We know
$3 x = 2 x + x$
$\Rightarrow cot 3 x = cot (2 x + x)$
$\Rightarrow cot 3 x = \frac{c o t 2 x \cdot c o t x - 1}{c o t 2 x + c o t x}$
$\Rightarrow cot 3 x cot 2 x + cot 3 x cot x = cot 2 x cot x - 1$
$\Rightarrow cot x cot 2 x - cot 2 x cot 3 x - cot 3 x cot x = 1$

Q. Find the value of cotx.cot2x−cot2x.cot3x−cot3x.cotx.

We know 3x=2x+x ⇒cot3x=cot(2x+x) ⇒cot3x=cot2x+cotxcot2x⋅cotx−1​ ⇒cot3xcot2x+cot3xcotx=cot2xcotx−1 ⇒cotxcot2x−cot2xcot3x−cot3xcotx=1

Q. Find the value of $cot x . cot 2 x - cot 2 x . cot 3 x - cot 3 x . cot x$ .

We know
$3 x = 2 x + x$
$\Rightarrow cot 3 x = cot (2 x + x)$
$\Rightarrow cot 3 x = \frac{c o t 2 x \cdot c o t x - 1}{c o t 2 x + c o t x}$
$\Rightarrow cot 3 x cot 2 x + cot 3 x cot x = cot 2 x cot x - 1$
$\Rightarrow cot x cot 2 x - cot 2 x cot 3 x - cot 3 x cot x = 1$