Question

if a+b+c=r and cos A=cosB.cosC .show that tan A =tanB+tanC​

Answer 1

Given A+B+C=π⟹A=π−(B+C)

And also given cosA=cosBcosC

⟹cos(π−(B+C))=cosBcosC

⟹−cosBcosC+sinBsinC=cosBcosC

⟹sinBsinC=2cosBcosC

⟹tanBtanC=2