TS EAMCET · Maths · Determinants
For \(\alpha, \beta \in[0,2 \pi]\) and \(\gamma \in[0, \pi)\) consider the system of equations
\(\begin{aligned}
& 2 \sin \alpha-\cos \beta+3 \tan \gamma=3 \\
& 4 \sin \alpha+2 \cos \beta-2 \tan \gamma=2 \\
& 6 \sin \alpha-3 \cos \beta+\tan \gamma=9
\end{aligned}\)
Then, which one of the following is true?
- A \(2 \alpha-\beta-\gamma=0\)
- B \(2 \alpha+\beta+\gamma=0\)
- C \(\alpha-2 \beta-\gamma=0\)
- D \(\alpha+2 \beta-\gamma=0\)
Answer & Solution
Correct Answer
(A) \(2 \alpha-\beta-\gamma=0\)
Step-by-step Solution
Detailed explanation
\(\text{(a) Given, } 2 \sin \alpha-\cos \beta+3 \tan \gamma=3\qquad\ldots\text{(i)}\) \( 4 \sin \alpha+2 \cos \beta-2 \tan \gamma=2\qquad\ldots\text{(ii)}\) \( 6 \sin \alpha-3 \cos \beta+\tan \gamma=9\qquad\ldots\text{(iii)}\) Let \(x=\sin \alpha, y=\cos \beta, z=\tan \gamma\)…
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