Question

If sec⁴X - sec²X = 3 then what is the value of tan⁴X + tan²X =?

Answer 1

tan2X(tan2X+1-1)
(sec2X -1)(sec2X )
sec4X -secX = 3

Answer 2

Answer:

$\tan^4x+\tan^2x=3$

Step-by-step explanation:

We are given,

$\sec^4x-\sec^2x=3$

WE need to calculate the value of $\tan^4x+\tan^2x$

$\sec^4x-\sec^2x=3$

Take sec²X common from left side, We get

$\sec^2x(\sec^2x-1)=3$     .............(1)

Using the trignometric identity, $\tan^2x+1=\sec^2$

Also, $\tan^2x=\sec^2-1$

Put in (1) and we get,

$(\tan^2x+1)(\tan^2x)=3$

Using Distributive property, [a(b+c)=ab+bc]

$\tan^4x+\tan^2x=3$

Thus,$\tan^4x+\tan^2x=3$