Answer:
Step-by-step explanation:
If the R.H.S. is cot(4A), given question is misprinted.
It should be,
[tex]\frac{1}{\text{tan3A+tanA}}-\frac{1}{\text{cot3A+cotA}}[/tex]
= [tex]\frac{1}{\text{tan3A+tanA}}-\frac{1}{{\frac{1}{\text{tan3A}}+\frac{1}{\text{tanA}}}}[/tex]
= [tex]\frac{1}{\text{tan3A+tanA}}-\frac{1}{\frac{\text{tanA+tan3A}}{\text{tanAtan3A}}}[/tex]
= [tex]\frac{1-\text{tanAtan3A}}{\text{tanA+tan3A}}[/tex]
= [tex]\frac{1}{\text{tan}(A+3A)}[/tex]
= cot(4A) [R.H.S.]
Hence proved.
