Question

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

• A. $(-1,-1)$
• B. $(-1,1)$
• C. $(1,-1)$
• D. $(1,1)$

Answer 1

The correct option is C

$(1,-1)$

Find the value of $\mathbf{(}\mathit{\alpha }\mathbf{,}\mathbf{}\mathit{\beta }\mathbf{)}$:

Given,

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

By comparing it with $\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{(}\mathit{A}\mathbf{}\mathbf{+}\mathbf{}\mathit{B}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{A}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{B}\mathbf{}\mathbf{–}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{A}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{B}$, we get

$\begin{array}{rcl}\alpha & =& 1,\\ \beta & =& -1\\ (\alpha ,\beta )& =& (1,-1)\end{array}$

Hence, the correct option is C.