Answer:
see explanation
Step-by-step explanation:
Using the identities
tanx = [tex]\frac{sinx}{cosx}[/tex] , cotx = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
[tex]\frac{tanx}{tanx+cotx}[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{sinx}{cosx}+\frac{cosx}{sinx} }[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{sin^2x+cos^2x}{cosxsinx} }[/tex]
= [tex]\frac{\frac{sinx}{cosx} }{\frac{1}{cosxsinx} }[/tex]
= [tex]\frac{sinx}{cosx}[/tex] × [tex]\frac{cosxsinx}{1}[/tex] ← cancel cosx on numerator/ denominator
= sin²x
= right side
