Question

if sec x + sec ^2x=1, then tan^2 x − tan^4x is​

Answer 1

sec x + sec² x = 1............. (given)

=> sec x = 1 - sec²x

since , 1 + tan²x = sec²x

=> ( 1 - sec²x ) = - tan²x ........ (1)

and , from (1) , sec x = - tan²x ............. (2)

squaring both sides,

=> sec²x = tan⁴x .............. (3)

(2) + (3) , we get ,

=> sec x + sec²x = -tan²x + tan⁴x = 1 ( as , given)

=> -tan²x + tan⁴x = 1

multiply -1 both sides ,

=> tan²x - tan⁴x = -1