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AP EAMCET · Maths · Trigonometric Ratios & Identities

In a \(\triangle \mathrm{ABC}\), if \(\sin ^2 \mathrm{~B}=\sin \mathrm{A}\) and \(2 \cos ^2 \mathrm{~A}=3 \cos ^2 \mathrm{~B}\), then the triangle is

  1. A acute angled
  2. B obtuse angled
  3. C right angled
  4. D equilateral
Verified Solution

Answer & Solution

Correct Answer

(B) obtuse angled

Step-by-step Solution

Detailed explanation

\(2(1 - \sin^2 \mathrm{A}) = 3(1 - \sin^2 \mathrm{B})\) \(2(1 - \sin^2 \mathrm{A}) = 3(1 - \sin \mathrm{A})\) \(2 \sin^2 \mathrm{A} - 3 \sin \mathrm{A} + 1 = 0\) \((2 \sin \mathrm{A} - 1)(\sin \mathrm{A} - 1) = 0\) \(\sin \mathrm{A} = 1 \text{ (reject as A=90 leads to C=0)}\) or…