Question

If $a=A_{\pi /2}(\alpha ,\beta ,\gamma )$, $b=A_{\pi /3}(\alpha ,\beta ,\gamma )$. Which of the following is true?

• A. $a=b$
• B. $a<b$
• C. $a>b$
• D. $2a=b$

Answer 1

The correct option is A $a=b$

Given $\alpha ,\beta ,\gamma ,\theta ϵR$.

Let $A_{\theta }(\alpha ,\beta ,\gamma )=\left|\begin{array}{ccc}\cos (\alpha +\theta )& \sin (\alpha +\theta )& 1\\ \cos (\beta +\theta )& \sin (\beta +\theta )& 1\\ \cos (\gamma +\theta )& \sin (\gamma +\theta )& 1\end{array}\right|$

So $a=A_{\pi /2}(\alpha ,\beta ,\gamma )$,

$b=A_{\pi /3}(\alpha ,\beta ,\gamma )$.

From above its clear that a will be equal to b

$\therefore a=b$