Menu Close

if-a-b-c-pi-tanA-tanB-tanC-tanA-tanB-tanC-FAILED-TO-CALCULATE-




Question Number 143890 by pandu last updated on 19/Jun/21
if a+b+c=π      tanA+tanB+tanC =tanA.tanB.tanC  FAILED TO CALCULATE
$${if}\:{a}+{b}+{c}=\pi\:\:\: \\ $$$$\:{tanA}+{tanB}+{tanC}\:={tanA}.{tanB}.{tanC} \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$
Answered by justtry last updated on 19/Jun/21
Answered by bobhans last updated on 19/Jun/21
 a+b = π−c  ⇒((tan a +tan b)/(1−tan a.tan c)) = −tan c  ⇒tan a + tan b =−tan c +tan a tan b tan c  ⇒tan a+tan b+tan c = tan a. tan b. tan c
$$\:\mathrm{a}+\mathrm{b}\:=\:\pi−\mathrm{c} \\ $$$$\Rightarrow\frac{\mathrm{tan}\:\mathrm{a}\:+\mathrm{tan}\:\mathrm{b}}{\mathrm{1}−\mathrm{tan}\:\mathrm{a}.\mathrm{tan}\:\mathrm{c}}\:=\:−\mathrm{tan}\:\mathrm{c} \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{a}\:+\:\mathrm{tan}\:\mathrm{b}\:=−\mathrm{tan}\:\mathrm{c}\:+\mathrm{tan}\:\mathrm{a}\:\mathrm{tan}\:\mathrm{b}\:\mathrm{tan}\:\mathrm{c} \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{a}+\mathrm{tan}\:\mathrm{b}+\mathrm{tan}\:\mathrm{c}\:=\:\mathrm{tan}\:\mathrm{a}.\:\mathrm{tan}\:\mathrm{b}.\:\mathrm{tan}\:\mathrm{c}\: \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *