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This is a question from the chapter trigonometry. Can any one solve it.

This is a question from the chapter trigonometry. Can any one solve it.           
 

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1 Answers

Snehal Jadhav
54 Points
5 years ago
In this question the need is to simplify both the equations first individually and then after certain amount of simplfication equating both of them.
STEP 1
Divide the first equation throughout by cos2\LARGE \Theta.
Then, the equation will be:
a tan2\LARGE \Theta + b = m(1 + tan2\LARGE \Theta)
By, simplyfication:
(a – m) tan2\LARGE \Theta = m – b.......(3)
STEP 2
Divide the first equation throughout by cos2\LARGE \Phi.
Then, the equation will be:
b tan2\LARGE \Phi + a = n(1 + tan2\LARGE \Phi)
By, simplyfication:
(b – n) tan2\LARGE \Phi = n-a ........(4)
STEP 3
Simplification of condition given:
a tan\LARGE \Theta = b tan\LARGE \Phi
tan2\LARGE \Theta/tan2\LARGE \Phi = b2/a2…......(5)
STEP 4
Divide equations (3) and (4), then inject the equation (5) in the new equation:
(a – m)(b2)(n – a) = (m – b)(a2)(b – n)
 
ab2n – mnb2 – a2b2 + amb2 = amb2 – a2mn – a2b2 + a2bn
 
ab2n + a2mn – mnb2 – nba2 = 0
 
a2n(m – b) + b2n(a – m) = 0
 
a2n (m – b)= b2n(m – a)
 
THE FINAL EQUATION IS:
 
a2/b2=(m-b)/(m-a)
 

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