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प्रश्न
In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is ______
विकल्प
right-angled
equilateral
isosceles
scalene
MCQ
रिक्त स्थान भरें
उत्तर
In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is isosceles.
Explanation:
By sine rule,
`a/sinA = b/sinB = k`
⇒ a = k sin A, b = k sin B
Now, `cosA/a = cosB/b`
⇒ `cosA/(k sinA) = cosB/(k sinB)`
⇒ `cosA/sinA = cosB/sinB`
⇒ sin A cos B - cos A sin B = 0
⇒ sin (A - B) = 0
⇒ A - B = 0
⇒ A = B
ΔABC is an isosceles triangle.
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