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If tan(b)={(sin(a)×cos(a)}÷(2+cos(a)^2 then prove that 3tan(a-b)=2tan(a)

If tan(b)={(sin(a)×cos(a)}÷(2+cos(a)^2 then prove that 3tan(a-b)=2tan(a)

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Dear student
 
Starting from the later part
 
tan (a-b) = 2 tan a
 
tan a - tan b / 1 + tan a tanb  =  2 tan a
tan a - tan b = 2 tan a + 2 tan²a tan b
 
- tan a / 1 + 2 tan²a = tanb
 
tan b = - sina / cos a/(1 + 2 sin²a/cos²a)
 
tan b = - sin a * cos a/ (cos² a + 2 sin²a)
 
tan b = - sina cos a / (2 - cos²a)
Arun
25763 Points
3 years ago
Sorry by mistake answer is submitted.
 
Actual equation is 3 tan (a-b) = 2 tana
 
Hence please take care of 3. I have forgotten that.
 
Hope it helps

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