Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 81884 by rajesh4661kumar@gmail.com last updated on 16/Feb/20

Commented by mind is power last updated on 16/Feb/20

$$applie$$$$wecanfindtriangle$$$$withe{sin}^{-}x,{sin}^{-}y,{sin}^{-}zanglewitheoriantation$$$$a+b+c=\pi$$$$\Rightarrow sin\left(a\right)cos\left(a\right)+sin\left(b\right)cos\left(b\right)+sin\left(c\right)cos\left(c\right)=2sin\left(a\right)sin\left(b\right)sin\left(c\right)..1?$$$$\Rightarrow sin\left(2a\right)+sin\left(2b\right)+sin\left(2c\right)=4sin\left(a\right)sin\left(b\right)sin\left(c\right)..2$$$$sin\left(2a\right)+sin\left(2b\right)=2cos(a-b)sin(a+b)$$$$sin\left(2c\right)=sin(2\pi -2a-2b)=-sin(2a+2b)=-2sin(a+b)cos(a+b)$$$$sin\left(2a\right)+sin\left(2b\right)+sin\left(2c\right)$$$$=2cos(a-b)sin(a+b)-2sin(a+b)cos(a+b)$$$$=2sin(a+b)(cos(a-b)-cos(a+b))$$$$=4sin\left(a\right)sin\left(b\right)sin(\pi -c)=4sin\left(a\right)sin\left(b\right)sin\left(c\right)$$$$2..proved\iff 1True$$$$fora={sin}^{-}\left(x\right),b={sin}^{-}\left(y\right),{sin}^{-}\left(z\right)=c$$$$sin\left(a\right)=x,cos\left(a\right)=\sqrt{1-x^2}......\Rightarrow$$$$1\iff x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com