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how do you solve this.prove: cos2A plus cosA divided by sin2A minus sinA equal to cos2A plus 1 divided by sinA

  • math -

    I think there's a typo in your equation. For example , plug in A = pi/4. You then have

    (0 + 1/√2)/(1 - 1/√2) = (0+1)/(1/√2)
    1/√2 *√2 /(√2 - 1) = √2
    1/(√2-1) = √2
    √2+1 = √2

    However, if you fix the right side to read (cosA+1)/sinA

    you have the left side:

    (cos^2 A - sin^2 A + cosA)/(2sinAcosA - sinA)

    (cos^2 A - (1 - cos^2 A) + cosA)/(2sinAcosA - sinA)

    (2cos^2 A + cosA - 1)/[sinA(2cosA - 1)

    (2cosA-1)(cosA - 1)/[(2cosA - 1)(sinA)]

    (cosA -1)/sinA

    Now if you plug in any angle, the equality holds.

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