Question

TanA/(1+tan²A)² + cotA/(1+cot²)² = sinAcosA
Prove​

Answer 1

Answer:

The solution of the question is given above:-

Answer 2

Step-by-step explanation:

Given that

$tan \: a \div (1 + ta {n}^{2} {)}^{2} + cot a\div (1 + co {t}^{2} {)}^{2} = sina \: cosa$

To prove

LHS=RHS

Solution

$lhs = \frac{tan \: a}{(1 + ta {n}^{2} {)}^{2} } + \frac{cota}{(1 + co {t}^{2} {)}^{2} }$

$= \frac{ \frac{sin \: a}{cos \: a} }{ (\frac{1}{co {s}^{2}a } {)}^{2} } + \frac{ \frac{cosa}{sin \: a} }{( \frac{1}{si {n}^{2} a} {)}^{2} }$

$= sin \: a \times cos \: a(si {n}^{2}a + co {s}^{2} a)$

$= sin \: a \times cos \: a$

hence LHS is equal to RHS.