Question

3. If
If (* sin o - cos e)
os 0) = 1 and
(cos 0 + sin e) =
y b
b
1, prove that
x y²
62
= 2.
92​

Answer 1

Answer:

Given sin(θ+α)=a⟹cos(θ+α)=  

1−a  

2

 

​  

 

sin(θ+β)=b⟹cos(θ+β)=  

1−b  

2

 

​  

 

cos(α−β)=cos(θ+α−(θ+β))=cos(θ+α)cos(θ+β)+sin(θ+α)sin(θ+β)=  

(1−a  

2

)(1−b  

2

)

​  

+ab

cos  

2

(α−β)=(1−a  

2

)(1−b  

2

)+a  

2

b  

2

+2ab  

(1−a  

2

)(1−b  

2

)

​  

=1−a  

2

−b  

2

+2a  

2

b  

2

+2ab  

(1−a  

2

)(1−b  

2

)

​  

 

So  

2cos  

2

(α−β)−1−4abcos(α−β)

=2−2a  

2

−2b  

2

+4a  

2

b  

2

+4ab  

(1−a  

2

)(1−b  

2

)

​  

−1−4a  

2

b  

2

−4ab  

(1−a  

2

)(1−b  

2

)

​  

 

=1−2a  

2

−2b  

2

Answer 2

Explanation:

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