# pre calc help! easy 10 points?

Verify the equation

Sec^4=tan^4-1+2sec^2x

Relevance
• 6 years ago

We will proceed form the right hand side.

RHS

= tan^4(x) - 1 + 2sec^2(x)

= tan^4(x) - 1 + 2{tan^2(x) + 1}.....using the equation {tan^2(x) + 1} = sec^2(x)

= tan^4(x) - 1 + 2tan^2(x) + 2

= tan^4(x) +2tan^(x) + 1

= tan^2(x) * [tan^2(x) + 2] + 1

now, we will split the 2 into (1 + 1) and use the equation {tan^2(x) + 1} = sec^2(x)

= [sec^2(x) - 1] * [sec^2(x) + 1] + 1

now, we will use the equation (a + b) * (a - b) = a^2 - b^2

where, a = sec^2(x) and b = 1

= [sec^2(x)]^2 - 1 + 1

= sec^4(x)

=LHS

Hence, LHS = RHS, as, tan^4(x) - 1 + 2sec^2(x) = sec^4(x)