SOLUTION: Find all real numbers in the interval [0,2pi] that satisfy the equation tan x sec x = sqrt2

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Question 766713: Find all real numbers in the interval [0,2pi] that satisfy the equation
tan x sec x = sqrt2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all real numbers in the interval [0,2pi] that satisfy the equation
tan x sec x = sqrt2
%28sin%28x%29%2Fcos%28x%29%29%281%2Fcos%28x%29%29=sqrt%282%29
%28sin%28x%29%2Fcos%5E2%28x%29%29=sqrt%282%29
sin%28x%29%2F%281-sin%5E2%28x%29%29=sqrt%282%29
sin(x)=√2-√2sin^2(x)
√2sin^2(x)+sin(x)-√2=0
solve for sin(x) using quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=√2, b=1, c=-√2
ans:
sin(x)=-√2 (reject, -1 ≤ sin(x) ≤ 1)
or
sin(x)=√2/2
x=π/4, 3π/4