Trigonometric elements MCQ Quiz in বাংলা - Objective Question with Answer for Trigonometric elements - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Apr 13, 2025
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যদি \(\rm m = \left[ \begin{array}{cc} 2 &0\\ 0&1\end{array}\right] and \ n= \left[ \begin{array}{cc} 0 &1\\ -2&0\end{array}\right]\) হয় তাহলে m sinθ + n cosθ এর নির্ণায়কের মান কত?
Answer (Detailed Solution Below)
Trigonometric elements Question 1 Detailed Solution
Download Solution PDFগণনা:
m sinθ + n cosθ = sin θ \(\rm \left[ \begin{array}{cc} 2 &0\\ 0&1\end{array}\right]\) + cos θ \(\rm \left[ \begin{array}{cc} 0 &1\\ -2&0\end{array}\right]\)
= \(\rm \left[ \begin{array}{cc} 2\sin θ &0\\ 0&\sin θ\end{array}\right]\) + \(\rm \left[ \begin{array}{cc} 0 &\cosθ\\ -2\cosθ&0\end{array}\right]\)
= \(\rm \left[\begin{array}{cc} 2\sin θ &\cos θ\\ -2\cos θ&\sin θ\end{array}\right]\)
এখন,
|m sinθ + n cosθ| = \(\rm \left| \begin{array}{cc} 2\sin θ &\cos θ\\ -2\cos θ&\sin θ\end{array}\right|\)
= \(2\sin^2\theta \) + \(\rm 2 cos^2\theta \)
= 2( \(\sin ^2 \theta +\cos^2\theta \) )
= 2
সুতরাং, বিকল্প (4) সঠিক।
Trigonometric elements Question 2:
যদি \(\rm m = \left[ \begin{array}{cc} 2 &0\\ 0&1\end{array}\right] and \ n= \left[ \begin{array}{cc} 0 &1\\ -2&0\end{array}\right]\) হয় তাহলে m sinθ + n cosθ এর নির্ণায়কের মান কত?
Answer (Detailed Solution Below)
Trigonometric elements Question 2 Detailed Solution
গণনা:
m sinθ + n cosθ = sin θ \(\rm \left[ \begin{array}{cc} 2 &0\\ 0&1\end{array}\right]\) + cos θ \(\rm \left[ \begin{array}{cc} 0 &1\\ -2&0\end{array}\right]\)
= \(\rm \left[ \begin{array}{cc} 2\sin θ &0\\ 0&\sin θ\end{array}\right]\) + \(\rm \left[ \begin{array}{cc} 0 &\cosθ\\ -2\cosθ&0\end{array}\right]\)
= \(\rm \left[\begin{array}{cc} 2\sin θ &\cos θ\\ -2\cos θ&\sin θ\end{array}\right]\)
এখন,
|m sinθ + n cosθ| = \(\rm \left| \begin{array}{cc} 2\sin θ &\cos θ\\ -2\cos θ&\sin θ\end{array}\right|\)
= \(2\sin^2\theta \) + \(\rm 2 cos^2\theta \)
= 2( \(\sin ^2 \theta +\cos^2\theta \) )
= 2
সুতরাং, বিকল্প (4) সঠিক।