calculus

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Solve:

sec(x)^2= 3tanx +1



*** It is suppose to be the sqaure root of 3 but i could find the symbol so just wrote the 3 without it but it is suppose to be the square root of 3 times tanx + 1

  • calculus -

    Rewrite this using the trig identity
    sec^2(x) = 1 + tan^2(x)

    Then treat tanx as a new variable, y

    1 + tan^2x = sqrt3*(tanx + 1)

    1 + y^2 = sqrt3*(y + 1)

    y^2 -sqrt3*y -(sqrt3 -1) = 0

    Solve the quadratic equation for y and then use x = arctan y to solve for x

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