Question 198688
*[Tex \LARGE \sin^2(\theta)+\sin^2(\theta)\cot^2(\theta)=1] ... Start with the given equation.



*[Tex \LARGE \sin^2(\theta)+\sin^2(\theta)\left(\frac{\cos^2(\theta)}{\sin^2(\theta)}\right)=1] ... Replace cotangent with cosine over sine. Recall: {{{cot(x)=cos(x)/sin(x)}}}



*[Tex \LARGE \sin^2(\theta)+\frac{\sin^2(\theta)\cos^2(\theta)}{\sin^2(\theta)}=1] ... Multiply



*[Tex \LARGE \sin^2(\theta)+\cos^2(\theta)=1] ... Cancel out the common terms.



*[Tex \LARGE 1=1] ... Use the identity *[Tex \LARGE \sin^2(\theta)+\cos^2(\theta)=1]



So this verifies the identity.