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The number of integral triplets (a, b, c...

The number of integral triplets (a, b, c) such thet `a+b cos 2x+c sin^(2)x=0` for all x, is

A

0

B

1

C

3

D

infinitelt many

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`a+bcos2x+c sin^(2)x=0` for all x
`impliesa+b+(c-2b)sin^(2)x=0` for all x
`impliesa+b=0and c-2b=0`
`impliesa=-bandc =2b`
Thus, the triplets are `(-b,b,2b), where b in R.`
Hence, there are infinitely many triplets.
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