If theeta =30°, verify that cos3theeta=4cos³theeta-3cos theeta.
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Solution :
Here I am using A instead of theta.
A = 30°
LHS = cos 3A
= cos ( 3 × 30 )
= cos 90°
= 0 ----( 1 )
RHS = 4cos³A - 3cosA
= 4 cos³ 30° - 3 cos 30°
= 4 × (√3/2 )³ - 3 × ( √3/2 )
= 4 × ( 3√3 )/8 - 3√3/2
= 3√3/2 - 3√3/2
= 0 ---( 2 )
Therefore ,
LHS = RHS
•••••
Here I am using A instead of theta.
A = 30°
LHS = cos 3A
= cos ( 3 × 30 )
= cos 90°
= 0 ----( 1 )
RHS = 4cos³A - 3cosA
= 4 cos³ 30° - 3 cos 30°
= 4 × (√3/2 )³ - 3 × ( √3/2 )
= 4 × ( 3√3 )/8 - 3√3/2
= 3√3/2 - 3√3/2
= 0 ---( 2 )
Therefore ,
LHS = RHS
•••••
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