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Question
In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is ______.
Options
an equilateral triangle
a right angled triangle
an isosceles triangle
an isosceles right angled triangle
Solution
In ∆ABC, if cos A = `(sinB)/(2sinC)`, then ∆ABC is an isosceles triangle.
Explanation:
cos A = `(sinB)/(2sinC)`
∴ cos A = `(bk)/(2ck)` ....(Sine rule)
Also, `(b^2 + c^2 - a^2)/(2bc) = b/(2c)` ....(Cosine rule)
∴ `(b^2 + c^2 - a^2)/b` = b
∴ b2 + c2 – a2 = b2
∴ c2 = a2
`\implies` c = a
`\implies` ∆ABC is an isosceles triangle
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