Question
Download Solution PDFIf A + B = C, then tan A tan B tan C = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A + B = C
Concept used:
tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)
Calculations:
According to the question,
A + B = C
Multiplying tan on both sides,
⇒ tan(A + B) = tanC
⇒ (tanA + tanB)/(1 - tanA.tanB) = tanC
⇒ tanA + tanB = tanC(1 - tanA.tanB)
⇒ tanA + tanB = tanC - tanC.tanA.tanB
⇒ tanC.tanA.tanB = tanC - (tanA + tanB)
⇒ tanC.tanA.tanB = tanC - tanA - tanB
∴ The value of tanC.tanA.tanB is tanC - tanA - tanB.
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