Question

if sin⁴A +sin²A = 1,
prove that
(i). 1/tan⁴A + 1/tan²A = 1
(ii). tan⁴A + tan²A = 1​

Answer 1

Answer:

hope it is correct answer and helpful answer

Answer 2

♡[Answer]♡

i) Sin^4A + sin^2A = 1prove that 1/tan^4A + 1/tan^2A = 1

= Sin^4A + sin^2A = 1

= Sin^4A = 1 - sin^2A = cos^2A

Or, sin^4A / cos^2A = 1

Or, tan^2A = 1/sin^2A

Or tan^2A = csc^2A

Or tan^2A = 1+cot^2A

Now multiplying each term by tan^2A, we get

= tan^4A = tan^2A+1

Or tan^4A - tan^2A = 1

ii) Sin^4A+sin^2A = 1 prove that tan^4A+tan^2A = 1

Probably you means if sin^2A+sin^4A = 1, then tan^2A - tan^4A = 1. The proof is given below:-

= Sin^2A+sin^4A = 1

= Sin^4A = 1 - sin^2A = cos^2

Or sin^2A / cos^2A = 1 / sin^2A

Or tan^2A = csc^2A

Or tan^2A = 1+cot^2A

Multiplying each term by tan^2A, we get

= tan^4A = tan^2A+1

Or tan^4A - tan^2A = 1

Hope it helps you!!!!

Please mark me as brainliest and thank my 10 answer!!!!!!