pre calc help! easy 10 points?

Verify the equation

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

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  • 6 years ago
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    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)

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