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Prove the following identities : cot (theta) cos (theta) = csc (theta) - sin (theta)
(tan - sin) + (1 - cos) = ( 1 - sec )

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Daedalusid
cotθcosθ = cscθ - sinθ
(cosθ/sinθ)cosθ = cscθ - sinθ
[(cosθ)^2]/sinθ = cscθ - sinθ
[1-(sinθ)^2]/sinθ = cscθ - sinθ
1/sinθ - sinθ = cscθ - sinθ
cscθ - sinθ = cscθ - sinθ





Jers15id
let x=theta(I don't have the theta symbol)

cotxcosx=cscx-sinx
since cot is [tex]\frac{cosx}{sinx}[/tex]
[tex]\frac{cosx}{sinx}(cosx)=cscx-sinx[/tex]
[tex]\frac{cos^2x}{sinx}=cscx-sinx[/tex]
since cos²x=1-sin²x
Substitute
[tex]\frac{1-sin^2x}{sinx}=cscx-sinx[/tex]
Separate the 1-sin²x
[tex]\frac{1}{sinx}-\frac{sin^2x}{sinx}=cscx-sinx[/tex]
[tex]\frac{1}{sinx}=cscx;[/tex]
cscx-sinx=cscx-sinx

Hope this helps =)

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