Question

If sin theta =a-b/a+b then find the value of tan (π/4+theta/2)

Answer 1

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Answer 2

Answer:

√a/b

Step-by-step explanation:

Let us suppose that theta= 2x.

Now it is given that,

sin 2x = a-b/a+b ,and,

we have to find y= tan(45° + x)= (1 + t)/(1-t).....(1) ,where t= tanx

By the use of another standard formula we get,

sin 2x= 2t/(1+t^2) where t= tanx as this thing is already mentioned.

So now,

2t/(1+t^2)= a-b/a+b.......(2)

Now, from the equation (1),

we can write by arranging, t= 2/(y+1) – 1.

After substituting this value of t into equation 2 we get,

(a+b)(1 – y^2)= (a – b)(1 + y^2)

or y^2= a/b

or y= √a/b

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