solve a trigonometric equation sqrt(3) sin(x)−cos(x)=sqrt(2)

Dana Russo 2022-09-07 Answered
3 sin x cos x = 2
I think to do :
( 3 sin x cos x = 2 ) 2
but i dont get anything. Or to divied by 3 :
( 3 sin x cos x = 2 ) 3
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Answers (2)

barquegese2
Answered 2022-09-08 Author has 11 answers
Hint:
3 sin x cos x = 2 sin π 3 sin x cos π 3 cos x = 2 2
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tonan6e
Answered 2022-09-09 Author has 2 answers
One of the R-Formulas, a set of formulas for combining such trigonometric expressions, says that
a sin x b cos x = R sin ( x α )
where
R = a 2 + b 2 , α = tan 1 b a
However, I doubt this solution expresses any room for creativity for this question specifically, as noted by first answer
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