If a is equal to 30 verify that cos 2a is equal to 1 - 2 sin square a
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Solution :
If A = 30
LHS = cos 2A
= cos ( 2 × 30 )
= cos 60°
= 1/2 ------( 1 )
RHS = 1 - 2sin²A
= 1 - 2 sin² 30°
= 1 - 2 × ( 1/2 )²
= 1 - 1/2
= 1/2------( 2 )
From ( 1 ) and ( 2 ) , we conclude
Cos 2A = 1 - 2sin²A
•••••
If A = 30
LHS = cos 2A
= cos ( 2 × 30 )
= cos 60°
= 1/2 ------( 1 )
RHS = 1 - 2sin²A
= 1 - 2 sin² 30°
= 1 - 2 × ( 1/2 )²
= 1 - 1/2
= 1/2------( 2 )
From ( 1 ) and ( 2 ) , we conclude
Cos 2A = 1 - 2sin²A
•••••
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