Question

How can I solve this question

Answer 1

B

Explanation:

1 + tan²X = sec²X

(1 - tan²X)/sec²X

cos²X - sin²X

cos2X

Integral of cos2X

= sin2X ÷ 2 + c

= ½sin2X + c

Answer 2

B.
`(1)/(2) sin2x + c`

Explanation:

`\int \frac{1 - { tan}^(2)x }{1 + { tan}^(2)x } dx \\ \\ = \int \frac{1 - \frac{ {sin}^(2)x }{ {cos}^(2)x } }{ {sec}^(2)x } dx\\ \\ = \int \frac{ {cos}^(2) x - {sin}^(2)x }{ {cos}^(2) x * {sec}^(2) x }dx \\ \\ = \int (cos \: 2x)/(1) dx \\ \\ = \int {cos \: 2x}dx \\ \\ = (1)/(2) sin2x + c`