Question

tanC loge 12. If A + B + C = 180º and sinA + sinB cos C= 0 then, prove that 2tanB + tanC = 0​

Answer 1

Step-by-step explanation:

A+B+C=180

LHS=sin2A+sin2B+sin2C

=2sin(A+B)cos(A−B)+2sinCcosC

=2sinCcos(A−B)+2sinCcosC

=2sinC(cos(A−B)+cosC)

=2sinC(cos(A−B)−cos(A+B))

=2sinC2sinAsinB

=4sinAsinBsinC

=RHS

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