Question

If tan^4x-tan^2x=1 then prove that sin^4x+sin^2x=1

Answer 1

Answer:

Step-by-step explanation:

Tan⁴x - Tan²x = 1

=> Tan⁴x = 1 + Tan²x  

=> Tan⁴x = Sec²x   (∵ 1 + Tan²x  = Sec²x)

=> Sin⁴x / Cos⁴x = 1/Cos²x

=> Sin⁴x = Cos⁴x / Cos²x

=> Sin⁴x = Cos²x

=> Sin⁴x = 1 - Sin²x  ( ∵ Cos²x = 1 - Sin²x)

=> Sin⁴x + Sin²x = 1

Hence proved.