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IF tan(k+a)/p=tan(k+b)/q=tan(k+c)/r ,then prove that: ((p+q)/(p-q))*sin 2 (a-b) +((q-r)/(q+r))*sin 2 (b-c)+((r+p)(r-p))*sin 2 (c-a)=0

IF   tan(k+a)/p=tan(k+b)/q=tan(k+c)/r     ,then    prove that: ((p+q)/(p-q))*sin2(a-b) +((q-r)/(q+r))*sin2(b-c)+((r+p)(r-p))*sin2(c-a)=0

Grade:11

1 Answers

Rahul askIITiansExpert.IITR
110 Points
10 years ago
the point here is to note that there is a certain rhythm in expressions

now

a/b=c/d

then, (a+b)/(a-b)=(c+d)/(c-d)

use this three times and write the expressiosn in the for form of tans and p,q etc

now put tan=sin/cos and transform

the procedure is length but will get you an expression which will be like sin2(a-b), since u know what the expanded form of sin(a-b) is.

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