Answer:
1
Step-by-step explanation:
sec⁴x-tan⁴x÷sec²x + tan²X
= sec⁴x-tan⁴x/sec²x + tan²X
= (sec²x)²-(tan²x)²/sec²x + tan²X
Using the difference of two square
a² - b² = (a+b)(a-b)
(sec²x)²-(tan²x)² = (sec²x + tan²X)(sec²x - tan²X)
= (sec²x)²-(tan²x)²/sec²x + tan²X
= (sec²x + tan²X)(sec²x - tan²X)/sec²x + tan²X
= sec²x - tan²X
Also sec²X = 1 + tan²X
Substitute
= 1 + tan²X- tan²X
= 1
Hence the value of the expression is 1
