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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If in triangle $A B C, \cos A=\frac{\sin B}{2 \sin C}$, then the triangle is
  • A
    Equilateral
  • ✓
    Isosceles
  • C
    Right angled
  • D
    Obtuse triangle
✓

Answer

Correct option: B.
Isosceles
(B) $\cos A =\frac{\sin B }{2 \sin C } \Rightarrow \frac{ b ^2+ c ^2- a ^2}{2 bc }=\frac{ b }{2 c }$
$\begin{array}{l}\Rightarrow b^2+c^2-a^2-b^2=0 \Rightarrow c^2=a^2 \\ \Rightarrow c=a \Rightarrow \text { Triangle is isosceles }\end{array}$

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