Question

1+tan²A/1+cot²A=tan²A. Show that ?

Answer 1

plz complete the question ...

Answer 2

$\huge {ANSWER }$

✳TO PROVE ✳

▶$\frac{1+{tan }^{2}A}{1+{cot}^{2}A} = {tan}^{2}A$

Taking left hand side,

▶$\frac{1+{tan }^{2}A}{1+{cot}^{2}A}$

${Since}$

$1+{tan }^{2}A ={sec}^{2}A$

$1+{cot }^{2}A ={cosec}^{2}$

▶$\frac{{sec }^{2}A}{{cosec}^{2}A}$

${Since,}$

${sec}^{2}A = \frac{1}{{cos}^{2}}$

${cosec}^{2}= \frac{1}{{sin}^{2}A}$

▶$\frac{1}{{cos}^{2}A} ÷ \frac{1}{{sin}^{2}A}$

▶$\frac{1}{{cos}^{2}A} \times \frac{{sin}^{2}A}{1}$

▶$\frac{{sin}^{2}A} {{cos}^{2}A}$

${Since,}$

$\frac{sinA}{cosA} = tanA$

Therefore,

▶$\frac{{sin}^{2}A} {{cos}^{2}A} = {tan}^{2}A$

◼HENCE PROVED