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March 29, 2017

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Transform the expression from the left to the right.

Tan A+ CotA to cscAsecA

  • Pre-Calculus - ,

    So we must transform tan(A) + cot(A) into csc(A)*sec(A).

    tan(A) + cot(A)
    Note that cot(A) is equal to 1/tan(A). Substituting,
    = tan(A) + 1/tan(A)
    = (tan^2 (A) + 1) / tan(A)
    Recall the pythagorean identity: tan^2 (A) + 1 = sec^2 (A). Also tan(A) = sin(A)/cos(A) and sec(A) = 1/cos(A). Substituting,
    = sec^2 (A) / tan(A)
    = sec^2 (A) * cos(A) / sin(A)
    = sec(A) / sin(A)
    Finally, 1/sin(A) = csc(A). Thus,
    = sec(A) * csc(A)

    Hope this helps~ :3

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