If $$p1$$,$$p2$$,$$p3$$ are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then $$cos$$⁡$$Ap1+$$$$cos$$⁡$$Bp2+$$$$cos$$⁡$$Cp3$$ is equal to

Question

If $$p1$$,$$p2$$,$$p3$$ are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then $$cos$$⁡$$Ap1+$$$$cos$$⁡$$Bp2+$$$$cos$$⁡$$Cp3$$ is equal to

Infinity Learn · Accepted Answer

We have,$$cos$$⁡$$Ap1+$$$$cos$$⁡$$Bp2+$$$$cos$$⁡$$Cp3=12$$Δ$$(acos$$⁡$$A+bcos$$⁡$$B+icos$$⁡$$C)=R$$Δ$$($$$$sin$$⁡Acos⁡$$A+$$$$sin$$⁡Bcos⁡$$B+$$$$sin$$⁡Ccos⁡$$C)=R2$$Δ$$($$$$sin$$⁡$$2A+$$$$sin$$⁡$$2B+$$$$sin$$⁡$$2C)=R4sin$$⁡Asin⁡Bsin⁡$$C2$$Δ$$=2Rsin$$⁡Asin⁡Bsin⁡CΔ$$=2R$$Δ×$$2$$Δbc×$$2$$Δca×$$2$$Δ$$ab=16R$$Δ$$2a2b2c2=16R$$Δ$$2(4R$$Δ$$)2=1R$$

If $p_{1}, p_{2}, p_{3}$ are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then $\frac{\cos A}{p_{1}} + \frac{\cos B}{p_{2}} + \frac{\cos C}{p_{3}}$ is equal to

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If p1,p2,p3 are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then cos⁡Ap1+cos⁡Bp2+cos⁡Cp3 is equal to

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If $p_{1}, p_{2}, p_{3}$ are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then $\frac{\cos A}{p_{1}} + \frac{\cos B}{p_{2}} + \frac{\cos C}{p_{3}}$ is equal to