Question

( (c) ptr-9 p-9-7 If tan n0 = tan mo, then the different values of 0 will be in RD​

Answer 1

Answer

Correct option is

A

4n

(n−1)  

2

 

​

 

tanθ=ntanϕ→1

tan(θ−ϕ)=  

1+tanθtanϕ

tanθ−tanϕ

​

→2

tan(θ−ϕ)=  

tanϕ

1

​

+tanθ

tanθ/tanϕ−1

​

 

=  

tanϕ

1

​

+ntanϕ

n−1

​

 

tan(θ−ϕ) will be maximum if  

tanϕ

1

​

+ntanϕ should be minimum, then

AM≥GM

2

tanϕ

1

​

+ntanϕ

​

≥  

tanϕ

1

​

×ntanϕ

​

 

2

tanϕ

1

​

+ntanϕ

​

≥  

n

​

 

tanϕ

1

​

+ntanϕ≥2  

n

​

 

tan(θ−ϕ)=  

2  

n

​

 

n−1

​

 

tan  

2

(θ−ϕ)=  

4n

(n−1)  

2

 

​