How to solve tan^2y sec^2y-tan^4y=tan^2y ?

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Answer 1 · 2018-04-03T01:55:46

Please see below.

#tan^2y sec^2y-tan^4y#

= #tan^2y sec^2y-tan^2ytan^2y#

= #tan^2y(sec^2y-tan^2y)#

= #tan^2yxx1#

= #tan^2y#

Answer 2 · 2018-04-03T02:01:16

As proved.

#" To prove " tan^2 y sec^2 y - tan^4y = tan^2 y#

#tan^2y sec^2y - tan^4Y#

#=> tan^2y (sec^2 y - tan^2y), " taking out common term " tan^2y#

#But sec^2 y - 1 = tan^2 y ' or " sec^2y - tan^1 y = 1#

#:. => tan^2y * 1 = tan^2 y = R H S#

#"Q E D"#