Question and Answers Forum

All Questions      Topic List

Coordinate Geometry Questions

Previous in All Question      Next in All Question      

Previous in Coordinate Geometry      Next in Coordinate Geometry      

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

$$\:\mathrm{a}+\mathrm{b}\:=\:\pi−\mathrm{c} \\ $$$$\Rightarrow\frac{\mathrm{tan}\:\mathrm{a}\:+\mathrm{tan}\:\mathrm{b}}{\mathrm{1}−\mathrm{tan}\:\mathrm{a}.\mathrm{tan}\:\mathrm{c}}\:=\:−\mathrm{tan}\:\mathrm{c} \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{a}\:+\:\mathrm{tan}\:\mathrm{b}\:=−\mathrm{tan}\:\mathrm{c}\:+\mathrm{tan}\:\mathrm{a}\:\mathrm{tan}\:\mathrm{b}\:\mathrm{tan}\:\mathrm{c} \\ $$$$\Rightarrow\mathrm{tan}\:\mathrm{a}+\mathrm{tan}\:\mathrm{b}+\mathrm{tan}\:\mathrm{c}\:=\:\mathrm{tan}\:\mathrm{a}.\:\mathrm{tan}\:\mathrm{b}.\:\mathrm{tan}\:\mathrm{c}\: \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com