Question

(tan(alpha))/(1 + tan^2 (alpha)) = (cot(alpha))/(1 + cot^2 (alpha))

Answer 1

Answer:

$Solve \: \: by \: \: converting \: \: tan \alpha \: \: to \: cot \alpha$

Step-by-step explanation:

$lhs = \frac{tan \alpha }{1 + tan^{2} \alpha } \\ = \frac{ \frac{1}{cot \alpha } }{1 + \frac{1}{cot^{2} \alpha } } \\ = \frac{ \frac{1}{cot \alpha } }{ \frac{cot^{2} \alpha + 1 }{cot ^{2} \alpha } } \\ = \frac{1}{cot \alpha } \times \frac{cot^{2} \alpha }{cot^{2} \alpha + 1 } \\ \frac{cot \alpha }{1 + cot^{2} \alpha } = rhs$