Given. cos(A-B)= cosAcosB +sinAsinB. value of cos15 A=60 and b= 30 verify
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Hi ,
If A = 60° , B = 45°
Cos15°
= Cos( 60 - 45 )
= Cos60cos45 + sin60sin45
= ( 1/2 )(1/√2 ) + ( √3/2)(1/√2)
=[1/2√2 + √3/2√2 ]
= ( 1+√3 ) / 2√2
2) if A = 60 , B = 30°
LHS = cos ( 60 - 30 )
= Cos30
= √3 /2
RHS = cos60cos30 + sin60sin30
= ( 1/2 )( √3/2 ) + ( √3/2 ) ( 1/2 )
= √3/4 + √3/4
= 2( √3/4 )
= √3/2
LHS = RHS
Hence proved .
I hope this helps you.
:)
If A = 60° , B = 45°
Cos15°
= Cos( 60 - 45 )
= Cos60cos45 + sin60sin45
= ( 1/2 )(1/√2 ) + ( √3/2)(1/√2)
=[1/2√2 + √3/2√2 ]
= ( 1+√3 ) / 2√2
2) if A = 60 , B = 30°
LHS = cos ( 60 - 30 )
= Cos30
= √3 /2
RHS = cos60cos30 + sin60sin30
= ( 1/2 )( √3/2 ) + ( √3/2 ) ( 1/2 )
= √3/4 + √3/4
= 2( √3/4 )
= √3/2
LHS = RHS
Hence proved .
I hope this helps you.
:)
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