If (A + B) = A B + A B, then ( , ) = - Vidyadip

MCQ

If $\cos (A + B) = \alpha \cos A\cos B + \beta \sin A\sin B,$ then $(\alpha ,\beta ) =$

A
$(-1, -1)$
B
$(-1, 1)$
✓
$(1, -1)$
D
$(1, 1)$

✓

Answer

Correct option: C.

$(1, -1)$

c
(c) Given $\cos \,(A + B) = \alpha \,\cos A\,\cos B + \beta \,\sin A\,\sin B$

But $\cos \,(A + B) = \cos \,A\,\cos B - \sin A\,\sin \,B$

$ \Rightarrow \,\,\alpha = 1,\,\,\beta = - 1.$

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