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

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

Trigonometric Functions

Solution:

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