solve trigonometric identity

Question

1-tan to the power of 4=2 sec to the power of 2 - sec to the power o4

Answer 1

1-tan⁴=2sec²-sec⁴

switch sides

2sec²-sec⁴=1-tan⁴

use the identity sec²=1+tan²

2(1+tan²)-(1+tan²)²=

2+2tan²-1-2tan²-tan⁴=

rearrange the terms on the left side

2-1+2tan²-2tan²-tan⁴=

1-tan⁴=1-tan⁴