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

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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#