Question

sec²x(sec²x-2)+1=tan⁴x

Answer 1

Hi ,

we know the trigonometric identity

sec² x = 1 + tan² x

Now ,

LHS = sec² x ( sec² x - 2 ) + 1

= ( 1 + tan² x ) [ 1+ tan² x - 2 ] +1

= ( 1 + tan² x )( tan² x - 1 ) + 1

= ( tan² x + 1 ) ( tan² x - 1 ) + 1

= [ ( tan² x )² - 1 ² ] + 1

since ( a + b ) ( a - b ) = a² - b²

= tan⁴ x - 1 + 1

= tan⁴ x

= RHS

I hope this helps you.

:)