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find the general solution of the equation 7cos 2 x+3sin 2 x=4

find the general solution of the equation 7cos2x+3sin2x=4

Grade:11

2 Answers

Arun
25750 Points
5 years ago
7 cos²x + 3 sin²x 
= 4 cos²x + 3 cos²x + 3 sin²x 
= 4 cos²x + 3 (cos²x + sin²x) 
= 4 cos²x + 3 

This can only be = 4 when 4 cos²x = 1, i.e. for only certain values of x. 
However, an identity (which you want us to prove) should be true for all values of x. 

So I believe that instead of this being an identity that needs to be proven, this is actually an equation that needs to be solved. Please be careful how you phrase your questions. 

7 cos²x + 3 sin²x = 4 
4 cos²x + 3 cos²x + 3 sin²x = 4 
4 cos²x + 3 (cos²x + sin²x) = 4 
4 cos²x + 3 = 4 
4 cos²x = 1 
cos²x = 1/4 
cosx = ±1/2 

x = π/3 + πk, 2π/3 + πk
prince sunjot dutt
58 Points
5 years ago
7 cos²x+3sin²x=4
7cos²x+3(1-cos²x)=4
7cos²x+3-3cos²x=4
4cos²x=1
Cosx=±1/2
Wkt:if
Cosx=cosa
Then, x=2nπ±a,______n€I
Cosx=cos(π/3) or Cosx=-cos(π/3)
X=2nπ±π/3       or x= 2nπ± 2π/3
                    n={±1,±2,±3,±4,±5.........)

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