Grade 11Trigonometry
plz help me to solv this. if A+B+C=pie ,cosA=cosBcosC , prove that tanA=tanB+tanC
plz help me to solv this. if A+B+C=pie ,cosA=cosBcosC , prove that tanA=tanB+tanC
1 Answer
Arun
R.H.S.
= tanB+tanC
= (sinB/cosB)+(sinC/cosC)
= (sinBcosC+cosBsinC)/(cosB.cosC)
= sin(B+C)/cosA [cosA=cosB.cosC]
= sinA/cosA [A+B+C=pie, B+C=pie-A, sin(B+C)=sin(pie-A)= sinA]
= tanA = L.H.S. Proved
= tanB+tanC
= (sinB/cosB)+(sinC/cosC)
= (sinBcosC+cosBsinC)/(cosB.cosC)
= sin(B+C)/cosA [cosA=cosB.cosC]
= sinA/cosA [A+B+C=pie, B+C=pie-A, sin(B+C)=sin(pie-A)= sinA]
= tanA = L.H.S. Proved
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