if √3 sin Φ- cos Φ=0 find the value of Φ.
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(√3sinA - cosa)=0
√(3^2+1^2)=2
=> 2(√3/2sina -1/2cosa)=0
We know that √3/2=cos30°
and 1/2=sin30°
so ....
2(cos30°sinA- sin30°cosA)=0
We know that cos@sinB - sin@cosB
= sin(B-@)
so....
2sin(A-30°)=0
=> sin(A-30°)=0
=> sin(A-30°)=sin(nπ)
=> A-30°=nπ
=> A=nπ +30°
Where n is an Integer (belongs to Z)
√(3^2+1^2)=2
=> 2(√3/2sina -1/2cosa)=0
We know that √3/2=cos30°
and 1/2=sin30°
so ....
2(cos30°sinA- sin30°cosA)=0
We know that cos@sinB - sin@cosB
= sin(B-@)
so....
2sin(A-30°)=0
=> sin(A-30°)=0
=> sin(A-30°)=sin(nπ)
=> A-30°=nπ
=> A=nπ +30°
Where n is an Integer (belongs to Z)
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