JEE Exam > JEE Questions > tan5x–tan 3x–tan2x =a)tan 5x tan 3x tan 2xb)c...
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tan5x–tan 3x–tan2x =
- a)tan 5x tan 3x tan 2x
- b)cos 5x cos 3x cos 2x
- c)sin 5x sin 3x sin 2x
- d)tan 8x tan 3x tan 2x
Correct answer is option 'A'. Can you explain this answer?
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tan5x–tan 3x–tan2x =a)tan 5x tan 3x tan 2xb)cos 5x cos 3x cos 2xc)sin ...
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tan5x–tan 3x–tan2x =a)tan 5x tan 3x tan 2xb)cos 5x cos 3x cos 2xc)sin ...
To prove that the correct answer is option 'A', let's simplify the expression tan5x – tan3x – tan2x and compare it with tan 5x tan 3x tan 2x.
Using the trigonometric identity tan(A - B) = (tanA - tanB) / (1 + tanA tanB), we can rewrite the expression as:
tan5x – tan3x – tan2x = tan(5x - 3x) - tan2x
= tan2x - tan2x
= 0
Now let's simplify tan 5x tan 3x tan 2x:
tan 5x tan 3x tan 2x = (tan 5x tan 3x) tan 2x
= (tan(5x + 3x) / (1 - tan(5x) tan(3x))) tan 2x
= tan(8x) / (1 - tan(5x) tan(3x)) tan 2x
Since tan 5x tan 3x tan 2x is not equal to zero in general, we can conclude that option 'A' is the correct answer.
Therefore, the correct answer is option 'A' (tan 5x tan 3x tan 2x).
Using the trigonometric identity tan(A - B) = (tanA - tanB) / (1 + tanA tanB), we can rewrite the expression as:
tan5x – tan3x – tan2x = tan(5x - 3x) - tan2x
= tan2x - tan2x
= 0
Now let's simplify tan 5x tan 3x tan 2x:
tan 5x tan 3x tan 2x = (tan 5x tan 3x) tan 2x
= (tan(5x + 3x) / (1 - tan(5x) tan(3x))) tan 2x
= tan(8x) / (1 - tan(5x) tan(3x)) tan 2x
Since tan 5x tan 3x tan 2x is not equal to zero in general, we can conclude that option 'A' is the correct answer.
Therefore, the correct answer is option 'A' (tan 5x tan 3x tan 2x).
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tan5x–tan 3x–tan2x =a)tan 5x tan 3x tan 2xb)cos 5x cos 3x cos 2xc)sin 5x sin 3x sin 2xd)tan 8x tan 3x tan 2xCorrect answer is option 'A'. Can you explain this answer?
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