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
- A acute angled
- B obtuse angled
- C right angled
- D equilateral
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…
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