Question

If A + B + C = 90°, show that
(i) tan A tan B + tan B tan C + tan C tan A = 1.​

Answer 1

Step-by-step explanation:

A+B+C=90

A+B=90-C

on multiply both side by tan

tan(A+B)=tan(90-C)

(tanA+tanB)/1-tanA•tanB= cotC

(tanA+tanB)/1-tanA•tanB= 1/tanC

(tanA+tanB)tanC=1-tanA•tanB

tanAtanC+tanBtanC=1-tanAtanB

tanAtanC+tanBtanC+tanAtanB=1

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