Homework Help: calculus

Posted by Jack on Monday, September 13, 2010 at 10:53pm.

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 - drwls, Tuesday, September 14, 2010 at 2:22am
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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