## Trending News

# Trigonometrical question?

Show that

if α, β and γ are three angles of a triangle then

sin2α + sin2β + sin2γ = 4 sinα sinβ sinγ

### 2 Answers

Relevance

- SergioLv 52 months agoFavorite Answer
γ = 180 - ( α + β ) ..... 2γ = 360 - ( 2α + 2β )

you start with these 2 sustitutions

then formulas prostaferesis and sum/difference of angles

- VamanLv 72 months ago
4 sin a sin b sinc= 2 sin c(sina sinb)= sin c ( cos (a-b)-cos(a+b))= sin (c) cos (a-b) - sin(c) cos (a+b)=( sin (c+a-b)+sin(c-a+b)-(sin(c+a+b)+sin(c-a-b)

now put the values. = (sin (pi-2b)+sin(pi-2a)+ sin pi+sin(2c-pi)=sin 2b+sin 2a+sin 2c. you expand sin terms and put values. you got the answer.

- Login to reply the answers

Still have questions? Get your answers by asking now.

A good explanation