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NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

What is 2 x 4 x- 4 x 6 x- 6 x 2 x equal to?

What is

\cot 2 x \cot 4 x-\cot 4 x \cot 6 x-\cot 6 x \cot 2 x

equal to?

Options

A $-1$
B $0$
C $1$
D $2$

Correct answer

C. $1$

Step-by-step solution

\begin{aligned} & \cot (6 x)=\cot (2 x+4 x) \\ & \Rightarrow \cot 6 x=\frac{\cot 2 x \cdot \cot 4 x-1}{\cot 2 x+\cot 4 x}\end{aligned}

\therefore \cot 2 x \cdot \cot 6 x+\cot 6 x \cdot \cot 4 x=\cot 2 x \cdot \cot 4 x-1

or,

\cot 2 x \cdot \cot 4 x-\cot 4 x \cdot \cot 6 x-\cot 6 x \cdot \cot 2 x=1$.

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