help18

See my (corrected) answer at http://web2.0calc.com/questions/if-a-b-c-pi-amp-cosa-cosb-cosc-then-prove#r2 

If  A+B+C=pi & cosA=cosB*cosC then prove that-

tanA=tanB+tanC

A  = pi - (B + C)     ......therefore.....

sin A = sin [(pi) - ( B + C) ]

sinA  = sin(pi)cos(B +C) - sin(B+ C)cos(pi)      ......    [ sin(pi) = 0,   cos(pi) = -1   ]

sinA  = sin(B + C)

sinA  =  [ sinBcosC + sinCcosB]

Therefore

tanA  = sinA/cosA          [given →   cosA = cosBcosC]

tanA  =  [ sinBcosC + sinCcosB] / [cosBcosC]      

tanA  = [sinBcosB]/ [cosBcosC] + [sinCcosB] / [cosBcosC]

tan A  = [sinB/cosC] + [ sinC/cosC]

tanA = tanB  + tanC