Question

If sin²A+ sin⁴A=1-
i. tan⁴A-tan²A=1
ii. tan⁴A+sec²A= 1
iii. tan⁴A= sec²A
Which one is correct? Please Explain.

Answer 1

Answer:-

sin ^4 A = 1 -sin ^2 A

sin^4 A = cos ²A [∵ 1-sin²a = cos²a]

sin^4A/cos^4A = cos²A / cos ^4A [ dividing each term with cos^4 A]

tan^4A = 1/cos ²A

tan ^4A = sec ²A  

tan ^4A = 1+ tan ² A  [ ∵ sec²a = 1+tan²A]

tan^4A - tan² A= 1

hence proved