Algebra2 Verify Identity

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Verify the Identity:
csc(x)+sec(x)/sin(x)+cos(x)=cot(x)+tan(x)

the left side of the equation is all one term.

  • Trig: use parentheses -

    Verify:
    (csc(x)+sec(x))/(sin(x)+cos(x))=cot(x)+tan(x)

    Left hand side
    (csc(x)+sec(x))/(sin(x)+cos(x))
    =(1/sin(x)+1/(cos(x))/(sin(x)+cos(x))
    =((cos(x)+sin(x))/(sin(x)cos(x))/(sin(x)+cos(x))
    =1/(sin(x)cos(x))

    Right hand side:
    cot(x)+tan(x)
    =cos(x)/sin(x) + sin(x)/cos(x)
    =(cos²(x) + sin²(x))/(sin(x)+cos(x))
    =1/(sin(x)+cos(x))

    So the identity is verified.

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