TS EAMCET · Maths · Trigonometric Equations
If \(\cot \theta+\tan \theta=3\) and \(1-\cos ^2 \theta-\alpha \cos \theta=0\), then
- A \(6 \alpha^2\left(9-\alpha^2\right)=1\)
- B \(6 \alpha^2\left(\alpha^2-9\right)=1\)
- C \(9 \alpha^2\left(6-\alpha^2\right)=1\)
- D \(9 \alpha^2\left(\alpha^2-6\right)=1\)
Answer & Solution
Correct Answer
(C) \(9 \alpha^2\left(6-\alpha^2\right)=1\)
Step-by-step Solution
Detailed explanation
If \(\cot \theta+\tan \theta=3\) \(\Rightarrow \quad \frac{1}{\sin \theta \cos \theta}=3\) \(\Rightarrow \quad 3 \sin \theta \cos \theta=1\) and \(\quad 1-\cos ^2 \theta-\alpha \cos \theta=0\) \(\Rightarrow \quad \sin ^2 \theta=\alpha \cos \theta\) From Eqs. (i) and (ii), we get…
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