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Question
cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to ______.
Options
– 1
0
1
`1/2`
MCQ
Fill in the Blanks
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Solution
cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to 1.
Explanation:
We know that, cot 3x = cot(2x + x)
`\implies` cot 3x = `(cot 2x cot x - 1)/(cot 2x + cot x)`
`\implies` cot 3x . cot 2x + cot 3x . cot x = cot 2x . cot x – 1
`\implies` cot 3x . cot 2x + cot 3x . cot x – cot 2x . cot x = – 1
`\implies` cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x = 1
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Trigonometric Functions of Triple Angle
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