Question

find the general solution of ( sin theta +2cos theta = 1)
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Answer 1

Answer:

Step-by-step explanation:

Consider the given equation.

sinθ+2cosθ=1       ……… (1)

 

On squaring both sides, we get

(sinθ+2cosθ)  

2

=1  

2

 

sin  

2

θ+4cos  

2

θ+4sinθcosθ=1

 

We know that

sin  

2

θ=1−cos  

2

θ

cos  

2

θ=1−sin  

2

θ

 

Therefore,

1−cos  

2

θ+4(1−sin  

2

θ)+4sinθcosθ=1

−cos  

2

θ+4−4sin  

2

θ+4sinθcosθ=0

−cos  

2

θ−4sin  

2

θ+4sinθcosθ=−4

4sin  

2

θ+cos  

2

θ−4sinθcosθ=4

(2sinθ−cosθ)  

2

=4

2sinθ−cosθ=2

 

Hence, proved.