Question

cos(A+B) = cosA + cosB.State whether the given statement is true or false. Justify your answer.

Answer 1

It is a false statement.

It can be proved false by taking an example of A = 30 deg and B = 60 deg

cos(90) = 0 and cos(30) = √3/2 and cos(60) = 1/2

Here cos(30) + cos(60) = (√3 + 1)/2 which is not equal to 0. Hence the statement is false.

Answer 2

Given statement ,

" Cos ( A + B ) = Cos A + Cos B "

is False .

Explanation :

If A = 30° , B = 60°

LHS = Cos ( A + B )

= Cos ( 30 + 60 )

= Cos 90°

= 0 ---( 1 )

RHS = Cos A + Cos B

= Cos 30° + Cos 60°

= √3/2 + 1/2

= ( √3 + 1 )/2 ---( 2 )

From ( 1 ) & ( 2 ),

LHS ≠ RHS

Therefore ,

Cos ( A + B ) ≠ Cos A + Cos B

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