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tan a and tan b are the toots of the equation X² - pX + q = 0 the nthe value of sin²(a+b)

tan a and tan b are the toots of the equation 
X² - pX + q = 0 the nthe value of sin²(a+b)
 

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Dear Vinit
 
tan a + tanb = p
tan a * tan b = q
 
 
tan(a+b) = tan a + tan b / (1 – tan a tanb)
 
 = p/ 1 – q
 
tan(a+b) = p /(1 – q)
 
sin (a+b) = p / \sqrt(p2 + (1 -q)2)
 
hence
 
sin2 (a+b) = p2 / (p2 + (1 -q)2)
Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
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