Prove that cot 2x cot x-cot 3x cot 2x-cot 3x cot x=1.

Question

Prove that [latex] \cot 2 x \cot x-\cot 3 x \cot 2 x-\cot 3 x \cot x=1 [/latex].

Accepted Answer

We have

[latex]\begin{aligned}& \cot 3 x=\cot (2 x+x) \\Leftrightarrow & \cot 3 x=\frac{\cot 2 x \cot x-1}{\cot 2 x+\cot x} \\Leftrightarrow & \cot 3 x \cot 2 x+\cot 3 x \cot x=\cot 2 x \cot x-1 \\Leftrightarrow & \cot 2 x \cot x-\cot 3 x \cot 2 x-\cot 3 x \cot x=1 .\end{aligned}[/latex]

Hence, [latex] \cot 2 x \cot x-\cot 3 x \cot 2 x-\cot 3 x \cot x=1 [/latex].

Question 15.4.19: Prove that cot 2x cot x-cot 3x cot 2x-cot 3x cot x=1....

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