NCERT Class XI Mathematics - Trigonometric Functions - Solutions
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Question : 39
Total: 61
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution:
We know that 3x = 2x + x.
Therefore, cot 3x = cot (2x + x) =
Since cot (A + 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
Therefore, cot 3x = cot (2x + x) =
Since cot (A + 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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