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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 39 of 61
Marks: +1, -0
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution:  
We know that 3x = 2x + x.
Therefore, cot 3x = cot (2x + x) = cot⁡2xcot⁡x−1cot⁡2x+cot⁡x\frac{\cot 2x \cot x - 1}{\cot 2x + \cot x}
Since cot (A + B) = cot⁡Acot⁡B−1xotA+cot⁡B\frac{\cot A \cot B - 1}{xotA + \cot B}
⇒ cot 3 x (cot 2x + cot x) = cot 2x cotx – 1
⇒ cot 2x cot 3x + cotx cot3x = cot 2x cotx – 1
⇒ cot 2x cot x – cot 2x cot 3x – cotx cot 3x = 1
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