5 tan ⁴x-1=4 tan² x.find general solution

Assume tan² x = a where a ' belongs to 'R

now , equation becomes 5 a ² - 4 a - 1 = 0

factorise and you'll get ( 5 a + 1 ) ( a - 1 ) = 0

= 5 a = -1 or a = 1

= a = ( - 1 / 5 ) or a =1

Since ,square of any function ( even negative numbers ) is never negative

so , a doesn't equal to ( - 1 / 5 ) and hence , a = 1 is true

= tan x = ± 1

this gives the general solution as { n ± ( / 4 ) } , where n ' belongs to ' Z