Solve for x: 3tan2x - 4tan3x = tansquare 3x. tan2x
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3 tan 2x - 4 tan 3x = tan² 3x * tan 2x
3 (tan 2x - tan 3x) = tan 3x + tan² 3x * tan 2x
= tan 3x (1 + tan 3x * tan 2x)
3 (tan 2x - tan 3x)/(1 + tan 3x * tan 2x) = tan 3x
3 * (- tan x) = tan 3x = (3 tan x - tan³ x) / (1 - 3 tan² x)
3 - tan² x = - 3 + 9 tan² x
tan x = + √3 /√5 or - √3/√5
x = 37.76125° or 142.23875°
3 (tan 2x - tan 3x) = tan 3x + tan² 3x * tan 2x
= tan 3x (1 + tan 3x * tan 2x)
3 (tan 2x - tan 3x)/(1 + tan 3x * tan 2x) = tan 3x
3 * (- tan x) = tan 3x = (3 tan x - tan³ x) / (1 - 3 tan² x)
3 - tan² x = - 3 + 9 tan² x
tan x = + √3 /√5 or - √3/√5
x = 37.76125° or 142.23875°
Answered by
1
Answer:
Step-by-step explanation:
Leftrightarrow3(tan2x−tan3x)=tan3x(tan3xtan2x+1)3(tan2x−tan3x)=tan3x(tan3xtan2x+1)
\Leftrightarrow3(sin2xcos2x−sin3xcos3x)=tan3x(sin3xsin2x+cos3xcos2xcos3xcos2x3(sin2xcos2x−sin3xcos3x)=tan3x(sin3xsin2x+cos3xcos2xcos3xcos2x
biến đổi bỏ mẫu được
−3sinx=tan3x.cosx−3sinx=tan3x.cosx
\Leftrightarrow−3sinx=sin3xcos3x.cosx−3sinx=sin3xcos3x.cosx
\Leftrightarrow−3sinx=sinx(3−4sin2x)cosxcos3x−3sinx=sinx(3−4sin2x)cosxcos3x
\Leftrightarrowsinx=0 hoặc
−3=(3−4sin2x)cosxcos3x=0−3=(3−4sin2x)cosxcos3x=0
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