In a triangle `A B C`, if `cos A=(sinB)/(2sinC)`, show that the triang – InterviewSolution

InterviewSolution

1.	In a triangle `A B C`, if `cos A=(sinB)/(2sinC)`, show that the triangle is isosceles.
Answer» `cos A = sinB/(2sinC)` `=>sinB = 2sinCcosA` As, `A+B+C = pi =>B = pi-(A+C)` `=>sin(pi-(A+C)) = 2sinCcosA` `=>sin(A+C) = 2sinCcosA` `=>sinAcosC +cosAsinC = 2sinCcosA` `=>sinAcosC -cosAsinC` `=>sin(A-C) = 0` `=>sin(A-C) =sin 0^@` `=>A-C = 0` `=> A= C` As, two of the angles of the triangle are equal, it means `Delta ABC` is an isoceles triangle.

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