How do you solve sqrt2tanx=2sinx?

1 Answer
Jan 8, 2017

Please see the explanation.

Explanation:

Subtract 2sin(x) from both sides:

sqrt(2)tan(x) - 2sin(x) = 0

Substitute sin(x)/cos(x) for tan(x):

sqrt(2)sin(x)/cos(x) - 2sin(x) = 0

Multiply both side by cos(x):

sqrt(2)sin(x) - 2sin(x)cos(x) = 0

Factor:

sin(x)(sqrt(2) - 2cos(x)) = 0

This is true when either factor is zero:

sin(x) = 0 and cos(x) = sqrt(2)/2

Use the inverse sine of the first root and the inverse cosine on the second root:

x = sin^-1(0) and x = cos^-1(sqrt(2)/2)

x = {(0 + npi),(pi/4 + 2npi),((7pi)/4 + 2npi):}

where n is any positive or negative integer, including 0.