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Please see attached image for the Question.This is a question from A Dasgupta IIT Mathematics.

Please see attached image for the Question.This is a question from A Dasgupta IIT Mathematics.

Question Image
Grade:9

1 Answers

Aditya Gupta
2080 Points
3 years ago
let alpha=a, beta=b, phi=p, theta=t, gamma=c
now, sin^2a=(1 – cosp)(1 – cost) [using cos2z=1 – sin^2z]
so  sin^2a= 1-cosp-cost+cospcost=1 – cosa(cosb+cosc)/cosbcosc+cos^2a/cosbcosc
or cosa(1+cosbcosc)=cosb+cosc
so cosa= (cosb+cosc)/(1+cosbcosc)......(1)
Now let f(x)=(1-cosx)/(1+cosx)
using cmponend and dividendo. to (1) and factoring, we get 
f(a)=f(b)*f(c)
but, f(x)=(1-cosx)/(1+cosx)= tan^2(x/2)
so, tan^2(a/2)=tan^2(b/2)*tan^2(c/2)
or  tan(a/2)= ± tan(b/2)*tan(c/2)

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