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If tanα and tanβ are the roots of the equation X² - px + 6 =0 the sin²(α+β) = ?

If tanα and tanβ are the roots of the equation   
X² - px + 6 =0 the sin²(α+β) = ?
 

Grade:11

2 Answers

Arun
25758 Points
4 years ago
 
Dear Vinit
 
tan a + tanb = p
tan a * tan b = 6
 
 
tan(a+b) = tan a + tan b / (1 – tan a tanb)
 
 = p/ 1 – 6
 
tan(a+b) = p /(1 – 6)
 
sin (a+b) = p / \sqrt(p2 + (1 -6)2)
 
hence
 
sin2 (a+b) = p2 / (p2 + 25 )
Deepak Kumar Shringi
askIITians Faculty 4407 Points
4 years ago
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