Analytical Geometry> in a triangle ABC, prove that a^2cotA + b...

in a triangle ABC,provethat a^2cotA + b^2cotb + c^2cotc = abc\\\\Rquestion is from the chapter properties of triangles

meghana p , 5 Years ago

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Aditya Gupta

Last Activity: 5 Years ago

note that sinA/a= sinB/b= sinC/c= 1/2R.

so a= 2RsinA, b= 2RsinB and c= 2RsinC

hence, a^2cotA + b^2cotb + c^2cotc= 4R^2(sin^2A*cosA/sinA + sin^2B*cosB/sinB + sin^2C*cosC/sinC)

= 2R^2(sin2A + sin2B + sin2C)

but by conditional identities we know that sin2A + sin2B + sin2C= 4sinAsinBsinC

so, RHS= 8R^2sinAsinBsinC= 8R^2*(a/2R)*(b/2R)*(c/2R)

= abc/R

kindly approve :))

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Analytical Geometry> in a triangle ABC, prove that a^2cotA + b...

in a triangle ABC,provethat a^2cotA + b^2cotb + c^2cotc = abc\\\\Rquestion is from the chapter properties of triangles

meghana p , 5 Years ago

Aditya Gupta

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