Question

show that tan⁴theta +tan²theta=sec⁴theta-sec²theta

Answer 1

RHS sec^4theta-sec^2theta

===(sec^2theta)^2-sectheta^2
===(1+tan^2)^2-sec^2
===1+tan^4+2tan^2-(1+tan^2) 
===1+tan^4+2tan^2-1-tan^2
===tan^4+tan^2. LHS PROVED...

HOPE IT HELP YOU....

Answer 2

Step-by-step explanation:

Given,

tan⁴∅+tan²∅=sec⁴∅-sec²∅

L.H.S

$→$sec⁴∅-sec²∅

$→$sec²∅(sec²∅-1)

$→$(1+tan²∅)(1+tan²-1)  [∴sec²∅-1+tan²∅]

$→$(1+tan²∅)(tan²∅)

$→$tan²∅+tan⁴∅

L.H.S=R.H.S