TS EAMCET · Maths · Trigonometric Equations
Number of solutions of the equation \(\tan ^2 x+3 \cot ^2 x=2 \sec ^2 x\) lying in the interval \([0,2 \pi]\) is
- A \(3\)
- B \(4\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(\tan^2 x + 3\cot^2 x = 2\sec^2 x \implies \tan^2 x + \frac{3}{\tan^2 x} = 2(1+\tan^2 x)\) \(\tan^2 x + \frac{3}{\tan^2 x} = 2 + 2\tan^2 x \implies \frac{3}{\tan^2 x} = 2 + \tan^2 x\) \(\text{Let } y = \tan^2 x \implies 3 = 2y + y^2 \implies y^2 + 2y - 3 = 0\)…
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