Solve the equation. (find all solutions of the equation in the interval

Yulia

Yulia

Answered question

2021-09-17

Solve the equation. (find all solutions of the equation in the interval (0,2π).
(7sin(2x)+7cos(2x))2=49

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-09-18Added 91 answers

Given
(7sin(2x)+7cos(2x))2=49
solution
(7sin(2x)+7cos(2x))2=49
72(sin(2x)+cos(2x))2=49
(sin(2x)+cos(2x))2=1
sin2(2x)+cos2(2x)+2sin(2x)cos(2x)=1
1+2sin(2x)cos(2x)=1
2sin(2x)cos(2x)=0
sin(2(2x))=0 (since, 2sinxcosx=sin2x)
sin4x=0
4x=sin10
4x=nπ,nZ
x=π4,2π4,3π4,4π4,5π4,6π4,7π4,8π4,.....
Therefore the solution are,
x=π4,π2,3π4,π,5π4,3π2,7π4
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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