JEE Exam > JEE Questions > 1+cos2x+cos4x+cos6x=a)2 cosx cos2x cos3xb)4 s...
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1+cos2x+cos4x+cos6x=
- a)2 cosx cos2x cos3x
- b)4 sinx cos2x cos3x
- c)4 cosx cos2x cos 3x
- d)4 cosx cos2x sin3x
Correct answer is option 'C'. Can you explain this answer?
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1+cos2x+cos4x+cos6x=a)2 cosx cos2x cos3xb)4 sinx cos2x cos3xc)4 cosx c...
Solution:
Given, cos2x cos4x cos6x
We know that,
cos2x = 2cosx² - 1
cos4x = 2cos²2x - 1 = 2(2cos²x - 1)² - 1 = 8cos⁴x - 8cos²x + 1
cos6x = 2cos³x - 3cosx = 2cosx(3cos²x - 1)
Substituting these values in the given expression, we get
cos2x cos4x cos6x = (2cosx² - 1)(8cos⁴x - 8cos²x + 1)(2cosx(3cos²x - 1))
Simplifying this expression, we get
cos2x cos4x cos6x = 4cosx cos2x cos3x (4cos²x - 3)
Therefore, option (c) is the correct answer - 4cosx cos2x cos3x.
Given, cos2x cos4x cos6x
We know that,
cos2x = 2cosx² - 1
cos4x = 2cos²2x - 1 = 2(2cos²x - 1)² - 1 = 8cos⁴x - 8cos²x + 1
cos6x = 2cos³x - 3cosx = 2cosx(3cos²x - 1)
Substituting these values in the given expression, we get
cos2x cos4x cos6x = (2cosx² - 1)(8cos⁴x - 8cos²x + 1)(2cosx(3cos²x - 1))
Simplifying this expression, we get
cos2x cos4x cos6x = 4cosx cos2x cos3x (4cos²x - 3)
Therefore, option (c) is the correct answer - 4cosx cos2x cos3x.
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1+cos2x+cos4x+cos6x=a)2 cosx cos2x cos3xb)4 sinx cos2x cos3xc)4 cosx cos2x cos 3xd)4 cosx cos2x sin3xCorrect answer is option 'C'. Can you explain this answer?
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