Question

show that tan2+tan4=sec4-sec2

Answer 1

Answeer

sec^2-1=tan^2    identity

tan^2+tan^4=sec^4-sec^2

LHS, sec^2-1+(tan^2)^2

          sec^2-1+(sec^2-1)^2

        sec^2-1[1+(sec^2-1)]

        sec^2-1{sec^2]

sec^4-sec^2=RHS

PROVED

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Left side →sec^4x−sec^2x

=1cos^4x−1cos^2x

=1−cos^2xcos^4x

=sin^2xcos^4x

=tan^2x(1cos^2x)

Apply the trig identity: 1cos^2x=(1+tan^2x), we get:

Left side →tan^2x(1+tan^2x)=tan^4x+tan^2x.

hpoe my answer was helpful!!!!!

:)