Answers 2
Answer:= 2sin(x)
Step-by-step explanation:
2sin(x)/cos(3x) = tan(3x) - tan(x)
Let's try to prove that 2sin(x) = sin(3x) - tan(x)cos(3x).
Using the identities sin(3x) ? 3sin(x) - 4sin³(x) and cos(3x) ? 4cos³(x) - 3cos(x),
sin(3x) - tan(x)cos(3x) = 3sin(x) - 4sin³(x) - tan(x)(4cos³(x) - 3cos(x))
= sin(x)(3 - 4sin²(x) - (4cos²(x) - 3))
= sin(x)(6 - 4(sin²(x) + cos²(x)))
= 2sin(x).
(The above is simpler than using the standard identity that gives tan(3x) in terms of tan(x).)
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Author:
clancyri3c
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5
2sin(x)/cos(3x) = tan(3x) - tan(x)
Let's try to prove that 2sin(x) = sin(3x) - tan(x)cos(3x).
Using the identities sin(3x) ? 3sin(x) - 4sin³(x) and cos(3x) ? 4cos³(x) - 3cos(x),
sin(3x) - tan(x)cos(3x) = 3sin(x) - 4sin³(x) - tan(x)(4cos³(x) - 3cos(x))
= sin(x)(3 - 4sin²(x) - (4cos²(x) - 3))
= sin(x)(6 - 4(sin²(x) + cos²(x)))
= 2sin(x).
(The above is simpler than using the standard identity that gives tan(3x) in terms of tan(x).)
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Author:
jonathanpaig
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