Question

(1 - tan / 1 -cot)^2 = tan^2​

Answer 1

Answer:

(1 - tan / 1 -cot)^2 = tan^2​

Step-by-step explanation:

$(\frac{1 - tan}{1 -cot} )^{2}= (\frac{1 - \frac{sin}{cos} }{1 - \frac{cos}{sin} })^{2}\\= (\frac{\frac{cos - sin }{cos} }{\frac{sin - cos}{sin} })^{2} \\=\frac{cos^{2} + sin^{2} - 2sincos}{cos^{2}} * \frac{sin^{2}}{sin^{2}+cos^{2}-2sincos} \\=\frac{sin^{2}(1-2sincos)}{cos^{2}(1-2sincos)}\\= \frac{sin^{2}}{cos^{2}} \\= tan^{2}$

Answer 2

$( \frac{1 - tan}{1 - cot} ) ^{2} \\ \\ = ( { \frac{ \frac{cos - sin}{cos} }{ \frac{sin - cos}{sin} } })^{2} \\ \\ = ( \frac{cos - sin}{cos} \times \frac{sin}{sin - cos} ) ^{2} \\ \\ = ( - \frac{sin}{cos} ) ^{2} \\ \\ = \frac{ {sin}^{2} }{ {cos}^{2} } \\ \\ = {tan}^{2}$