Prove the identity: cos(x) cot(x) + sin(x) = csc(x)
C ChelseaF New member Joined Feb 20, 2007 Messages 1 Feb 20, 2007 #1 Prove the identity: cos(x) cot(x) + sin(x) = csc(x)
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Feb 20, 2007 #2 Re: Trig Identities. Hello, ChelseaF! Prove the identity: \(\displaystyle \:\cos(x)\cdot\cot(x)\,+\,sin(x)\:=\:\csc(x)\) Click to expand... The left side is: \(\displaystyle \L\:\cos(x)\cdot\frac{\cos(x)}{\sin(x)}\,+\,\sin(x) \;=\;\frac{\cos^2(x)}{\sin(x)}\,+\,\sin(x)\) . . . \(\displaystyle \L=\;\frac{\cos^2(x)}{\sin(x)}\,+\,\frac{\sin^2(x)}{\sin x} \;=\;\frac{\cos^2(x)\,+\,\sin^2(x)}{\sin(x)} \;=\;\frac{1}{\sin(x)}\;=\;\csc(x)\)
Re: Trig Identities. Hello, ChelseaF! Prove the identity: \(\displaystyle \:\cos(x)\cdot\cot(x)\,+\,sin(x)\:=\:\csc(x)\) Click to expand... The left side is: \(\displaystyle \L\:\cos(x)\cdot\frac{\cos(x)}{\sin(x)}\,+\,\sin(x) \;=\;\frac{\cos^2(x)}{\sin(x)}\,+\,\sin(x)\) . . . \(\displaystyle \L=\;\frac{\cos^2(x)}{\sin(x)}\,+\,\frac{\sin^2(x)}{\sin x} \;=\;\frac{\cos^2(x)\,+\,\sin^2(x)}{\sin(x)} \;=\;\frac{1}{\sin(x)}\;=\;\csc(x)\)
