Question
Download Solution PDFIf A, B and C are angles of a triangle, then which of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A, B and C are angles of a triangle .
Concept:
Use formula
\(\rm tan(A+B)= \frac{tanA+tanB}{1-tanA\cdot tanB}\)
Calculation:
A, B and C are angles of a triangle
then A + B +C = π
⇒ A + B = π - C
tan(A + B) = tan(180 - C)
\(\rm \implies \frac{tanA+tanB}{1-tanA\cdot tanB}=-\frac{tanC}{1}\)
⇒ tanA + tanB = -tanC + tanA tanB tanC
⇒ tan A + tanB +tanC = tanA tanB tanC
Hence the option (4) is correct.
Last updated on May 26, 2025
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