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if A and B are the solutions of 6cos thita+8sin thita=9 then sin(A+B) ?

if A and B are the solutions of 6cos thita+8sin thita=9 then sin(A+B) ?

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1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Rupali,

 

As A,B are both solutions of this equation,

 

We have 6CosA + 8SinA = 6CosB + 8SinB

or 6(cosA-cosB) = 8(sinB-sinA)

or 6*2*sin(B-A)/2*sin(B+A)/2 = 8*2Sin(B-A)/2*cos(B+A)/2

or tan(A+B)/2 = 8/6 = 4/3

 

Now Sin2X = 2tanx/(1+tan^2x)

 

Henc Sin(A+B) = [ 2*(4/3) ] / [1 + (4/3)^2] = 24/25.

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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