Question

(1+ cot² a)/(1+ tan² a) =?​

Answer 1

Answer:

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Answer 2

Answer:

$= { \csc}^{2}a \: { \cos }^{2} a$

Step-by-step explanation:

$\implies \frac{ 1 + \cot^{2} a }{1 + { \tan }^{2}a }$

We know,

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

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

now,

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

$= \frac{1 + { \cot }^{2}a }{ { \sec }^{2} a}$

$= \frac{ { \csc}^{2}a }{ { \sec }^{2} a}$

$= { \csc }^{2} a \times \frac{1}{ \sec^{2}a }$

$= { \csc}^{2}a \: { \cos }^{2} a$

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