If $sin2A+sin4A=1$ then prove that $tan^2A-tan^4A=1$ ?

Question

15756 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-21T17:26:31

Please see below.

Probably you mean if $sin^2A+sin^4A=1$ , then $tan^2A-tan^4A=1$ . The proof is as follows:

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

$hArrsin^4A=1-sin^2A=cos^2A$

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

If sin2A+sin4A=1sin2A+sin4A=1 then prove that tan^2A-tan^4A=1tan^2A-tan^4A=1?