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Trigonometry

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Solve the trigonometric equations.
1.) SIN²x(CSC²x-1)
2.) COT x SEC X
3.) COS²[(π/2)-x]/COS X

(Note: These mathematical problems are somewhat tricky, but useful for students as of learning how to their fundamental identities. Let's enjoy solving these problems!)

  • Trigonometry -

    You have no equations to solve, you probably meant "simplify the expressions"

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

    2. (cosx/sinx) (1/cosx)
    = 1/sinx
    = cscx

    3. recall the property of complementary trig ratios, that is...
    sin(π/2 - x) = cosx and cos(π/2 - x) = sinx
    sec(π/2 - x) = cscx and .....
    tan(π/2 - x) = cotx

    notice the names:
    sine --co-sine or cosine
    tangent -- co-tangent or cotangent
    secant --- co-secant or cosecant
    e.g. sin (90° - 20°) = sin 70° = cos20°

    so your question:
    COS²[(π/2)-x]/COS X
    = sin^2 x / cosx
    = (sinx)(sinx/cosx)
    = sinx tanx

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