Question

[1 - tan squared A] divided by [1 + cot squared A] URGENT!!!! PLS ANS FAST

Answer 1

Answer:-

To find:

(1 - tan² A)/(1 + cot² A) = ?

We know that,

Cosec² A - Cot² A = 1

→ Cosec² A = 1 + Cot² A

Hence,

→ (1 - tan² A)/(Cosec² A) = ?

Using tan² A = Sin² A/Cos² A and Cosec² A = 1/Sin² A in LHS we get,

$\sf \implies \large{ \frac{1 - \frac{ { \sin }^{2}A}{ \cos ^{2} A } }{ \frac{1}{ { \sin }^{2} A} } = \: ?}$

$\sf \implies \large{ \frac{ { \cos }^{2}A - { \sin }^{2} A }{ { \cos }^{2} A} \times { \sin}^{2} A}$

$\sf \implies \: ({ { \cos }^{2} A} - { \sin }^{2} A)( { \tan}^{2} A)$

We know that,

Sin² A + Cos² A = 1

→ Sin² A = 1 - Cos² A

→ - Sin² A = Cos² A - 1

$\sf \implies \: ( { \cos }^{2} A + { \cos }^{2} A - 1)( { \tan }^{2}A)$

$\sf \implies \: (2 { \cos}^{2} A - 1)( { \tan}^{2} A)$

$\sf \implies \: 2 { \cos }^{2} A \times \frac{ { \sin}^{2} A}{ { \cos }^{2} A} - { \tan }^{2} A$

→ 2Sin² A - tan² A

Answer 2

Step-by-step explanation:

see the answer carefully