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Quick Trig question? Trig Identities!?

Okay so I have to make this : sec^2x-sin^2x resemble this: cos^2x+tan^2x

Using trig identities

I did many other problems similar to this but, for some odd reason I am having trouble with this question.

Steps would be most gratefull!

Thank you!

1 Answer

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  • morgan
    Lv 7
    8 years ago
    Favorite Answer

    Given:

    sec^2(x) - sin^2(x) = cos^2(x) + tan^2(x)

    Would it be sufficient to show that the

    two sides are equal? That's easier than

    just converting the left side to be the

    right side.

    Add sin^2(x) to both sides:

    sec^2(x) = cos^2(x) + tan^2(x) + sin^2(x)

    Subtract tan^2(x) from both sides:

    sec^2(x) - tan^2(x) = cos^2(x) + sin^2(x)

    Apply the identity: sin^2 + cos^2 = 1

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

    Multiply both sides by cos^2(x)

    sec^2(x)*cos^2(x) - tan^2(x)*cos^2(x) = cos^2(x)

    1 - sin^2(x) = cos^2(x)

    Add sin^2(x) to both sides of the equation:

    1 = sin^2(x) + cos^2(x)

    Apply the identity sin^2 + cos^2 = 1

    1 = 1

    done.

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