Question

Find
Sin²A+1/1+tan²A​

Answer 1

Answer:

1

Step-by-step explanation:

Sin²A+1/1+tan²A​

= Sin²A + 1/Sec²A  (∵ 1 + Tan²A = Sec²A)

= Sin²A + Cos²A

= 1

Answer 2

Question:

$\sf Find: \ sin^{2}A \ + \ \dfrac{1}{1 \ + \ tan^{2}A}$

Solution:

$\implies \sf sin^{2}A \ + \ \dfrac{1}{1 \ + \ tan^{2}A}$

$\boxed {\sf{We \ know \ that, \ 1 \ + \ tan^{2}A = sec^{2}A }}$

$\implies \sf sin^{2}A \ + \ \dfrac{1}{sec^{2}A}$

$\boxed{\sf{We \ know \ that, \ \dfrac{1}{sec^{2}A} = cosec^{2}A}}$

$\implies \sf sin^{2}A + cosec^{2}A$

$\boxed{\sf{We \ know \ that, \ sin^{2}A + cosec^{2}A \ = \ 1}}$

$\implies \sf 1$

$\rule{400}{1}$

$\boxed {\sf sin^{2}A \ + \ \dfrac{1}{1 \ + \ tan^{2}A} = 1}$