Question

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

Answer 1

Given

secx + sec²x = 1

To find

tan²x - tan⁴x

secx + sec²x = 1

We know that sec²∅ - tan²∅ = 1

⇒ sec²x - tan²x = 1

Hence,

secx + sec²x = sec²x - tan²x

⇒ secx = - tan²x

Squaring both the sides,

⇒ sec²x = tan⁴x

Now, secx + sec²x = 1

⇒ - tan²x + tan⁴x = 1

Multiply with negative 1 on both sides

⇒ - 1(-tan²x + tan⁴x) = -1

⇒ tan²x - tan⁴x = -1

Hence, tan²x - tan⁴x = -1

Answer 2

Answer:

-1

Step-by-step explanation:

by simplyfying the equation we get secx=tan^2x

=tan^2x-tan^4x

=secx-sec^2x

=(cosx-1)/cos^2x

=tan^2x-sec^2x

=-1

we know : tan^2x + 1 = sec^2x