Question

tan 7θ . tan 3θ = 1 , Find the value of θ​

Answer 1

Answer ⤵️⤵️⤵️

We are given the question that tan7θ. tan3θ=1. Since, the denominator on RHS is 0, hence it is undefined and we denote undefined by the term 'infinity'. We know that tangent is infinity at π2.

Consider the given equation.

tan7θ⋅tan3θ=1

cos7θsin7θ⋅cos3θsin3θ=1

sin7θ⋅sin3θ=cos7θ⋅cos3θ

cos7θ⋅cos3θ−sin7θ⋅sin3θ=0

 

We know that

cos(A+B)=cosAcosB−sinAsinB

 

So,

cos(7θ+3θ)=0

cos(10θ)=0

cos(10θ)=cos2π

10θ=2nπ±2π

θ=5nπ±20π

 

Hence, the value of θ is 5nπ±20π.

Hope it helps ❤️༄