Question

given that cosα=1/2 and sinβ =1/2 then tan (α+β)=​

Answer 1

Answer:

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Step-by-step explanation:

Given θ is the arithmetic mean of α and β

⇒θ=  

2

α+β

​  

 

Also given cosα+cosβ=  

2

3

​  

 

⇒2cos(  

2

α+β

​  

)cos(  

2

α−β

​  

)=  

2

3

​  

 

⇒2cosθcos(  

2

α−β

​  

)=  

2

3

​  

          .....(1)

sinα+sinβ=  

2

1

​  

 

⇒2sin(  

2

α+β

​  

)cos(  

2

α−β

​  

)=  

2

1

​  

 

⇒2sinθcos(  

2

α−β

​  

)=  

2

1

​  

          .....(2)

Dividing (1) by (2), we get

cotθ=3

cosθ=  

10

​  

 

3

​  

 

sinθ=  

10

​  

 

1

​  

 

Now,  sin2θ+cos2θ=2sinθcosθ+1−2sin  

2

θ

=  

10

6

​  

+1−  

10

2

​  

 

=  

5

7

​  

              (Since maximum value sin2θ+cos2θ is 2)