Question

show that tan²x+tan⁴x=sec⁴x-sec²x​

Answer 1

Answer:

tan²x + tan⁴x = sec⁴x – sec²x

Step-by-step explanation:

LHS:

tan²x + tan⁴x

= (1 – sec²x) + tan⁴x

= 1 – sec²x + tan⁴x

= 1 + tan⁴x – sec²x

= (1 + tan⁴x) – sec²x

= sec⁴x – sec²x

hence, LHS=RHS (Proved).