Question

1+tan^2 A/1+cot^2 A=​

Answer 1

Answer:

tan²A

Step-by-step explanation:

$\frac{1+tan^{2}A }{1+cot^{2}A}\\= \frac{sec^{2}A }{cosec^{2}A}\\= \frac{sin^{2}A }{cos^{2}A}\\= tan^{2}A$

Answer 2

Question:

1+tan^2 A/1+cot^2 A=

Answer:

$\longrightarrow$$\frac{1 + { \tan(a) }^{2} }{1 + { \cot(a) }^{2} }$

we know that

$\longrightarrow$$1 + { \tan(a) }^{2} = { \sec(a) }^{2}$

$\longrightarrow$$1 + { \cot(a) }^{2} = { \cosec(a) }^{2}$

So, it bcms

$\implies$$\frac{1 + { \tan(a) }^{2} }{1 + { \cot(a) }^{2} } = \frac{ { \sec(a) }^{2} }{ { \cosec(a) }^{2} }$

$\implies$$\frac{ { \frac{1}{ \cos(a) } }^{2} }{ { \frac{1}{ \sin(a) } }^{2} }$

$\implies$${ \frac{ \sin(a) }{ \cos(a) } }^{2}$

$\longrightarrow$${ \tan(a) }^{2}$

$\huge \tt \underline \orange {Answer=\: tan(a)²}$

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Additional Information:

• 1 + sin²a = cos²a

• 1 + tan²a = sec²a

• 1 + cot²a = cosec²a