Question

Buktikan!?

1-tan² x / 1+tan² x = 2 cos² x-1
^_^

Tolong kerjakan kak ,secepatnya ​

Answer 1

1-tan^2x/1+tan^2x

=1-(sec^2x-1)/1+(sec^2x-1)

=2-sec^2x/sec^2x

=2/sec^2x-1

=2/1/cos^2x -1

=2cos^2x-1

(Terbukti)

Answer 2

Penjelasan dengan langkah-langkah:

1 - tan²x/ 1 + tan²x =

1 - (sin²x/cos²x) / (1 + (sin²x /cos²x))

((Cos²x - sin²x)/cos²x) / ((cos²x + sin²x)/cos²x)

= (cos²x - sin²x) / (cos²x + sin²x)

= cos²x - sin²x / 1

= cos²x - ( 1 - cos²x)

= cos²x + cos²x -1

= 2 cos²x - 1 ✔

Catatan :

Identitas trigonometri :

cos²x + sin²x = 1

Sin²x = 1 - cos²x

Tan²x = sin²x / cos²x