Question

If A + B + C = pi and cos A = cos B cos C then prove that tan A = tan B + tan C​

Answer 1

Step-by-step explanation:

LHS =tanB+tanC=

cosB

sinB

+

cosC

sinC

=

cosBcosC

cosCsinB+sinVcosB

=

cosA

sin(B+C)

[GivencosBcosC=cosA]

cosA

sin(180−A)

=tanA=RHS

Here proved

Answer 2

Answer:

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