Question

If sin 0 + cos 0 =y, and cos - sin 6 = x, then x 2 + y 2 is equal to​

Answer 1

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Step-by-step explanation:

sinθ+cosθ=x

⇒sin  

2

θ+cos  

2

θ+2sinθcosθ=x

⇒1+2sinθcosθ=x

⇒sinθcosθ=(x−  

2

1

​

)

sin  

6

θ+cos  

6

θ=(sin  

2

θ)  

3

+(cos  

2

θ)  

3

=(sin  

2

θ+cos  

2

θ)(sin  

4

θ+cos  

4

θ−sin  

2

θcos  

2

θ)

=((sin  

2

θ+cos  

2

θ)  

2

−2sin  

2

θcos  

2

θ−sin  

2

θcos  

2

θ)=1−3sin  

2

θcos  

2

θ

=1−  

4

3(x−1)  

2

 

​

 

=  

4

4−3(x−1)  

2

 

​

.