Question

Please solve this immediately!​

Answer 1

$\sf sec^4 x - sec^2 x = tan^4 c+ tan^2 x$

• Taking R.H.S.

$\sf →sec^4 x - sec^2 x$

Now,

• ( taking sec²x common )

$\sf→ sec^2 x ( sec^2x -1 )$

$\sf →sec^2x × tan^2 x$

we know,

$\sf (sec^2 - tan^2 x = 1)$

$\sf →(1+ tan^2x ) tan^2x$

another identity we know,

$\sf ( sec^2x = 1+ tan^2x )$

$\sf → tan^2x + tan^4x$ L.H.S

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Identity used

• $\sf (sec^2 - tan^2 x = 1)$
• $\sf ( sec^2x = 1+ tan^2x )$