Prive that: tan /(1+ tan^2)^2 +cot/(1+cot^2)^2 =sin×cos

1.	Prive that: tan /(1+ tan^2)^2 +cot/(1+cot^2)^2 =sin×cos
Answer» LHS\xa0{tex}=\\frac{\\tan A}{\\left(1+\\tan ^{2} A\\right)^{2}}+\\frac{\\cot A}{\\left(1+\\cot ^{2} A\\right)^{2}}{/tex}{tex}=\\frac{\\tan A}{\\left(\\sec ^{2} A\\right)^{2}}+\\frac{\\cot A}{\\left(\\ cosec ^{2} A\\right)^{2}}{/tex}{tex}=\\frac{\\sin A}{\\cos A}{/tex}\xa0. cos4\xa0A\xa0{tex}+\\frac{\\cos A}{\\sin A}{/tex}\xa0.\xa0sin4\xa0A= sin A cos3\xa0A + cos A sin3\xa0A= cos A sin A (cos2\xa0A + sin2\xa0A)= sin A cos A = RHS\xa0

Discussion