If #sin^4A+sin^2A=1#, prove that #tan^4A-tan^2A=1#?

1 Answer
Dec 19, 2017

Please see below.

Explanation:

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

#hArrsin^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#