solve the equation cos^x=sin^x+1

Supposing that you want to solve the equation cos x = sin x + 1,
we'll start by saying that this equation is linear and we'll re-write it moving the function sin
x, to the left.

cos x - sin x = 1

We'll
solve the equation using a helping angle:

We'll write the
coefficient of sin x, namely 1, as the tangent function of pi/4
angle.

We'll re-write the equation:

cos
x - tan(pi/4)*sin x = 1

But tan pi/4 = sin pi/4/cos
pi/4

cos x - (sin pi/4/cos pi/4)*sin x =
1

cos x*cos pi/4 - sin x*sin pi/4 = cos
pi/4

cos (pi/4 + x) = sqrt2/2

pi/4 + x
= +/-arccos (sqrt2/2) + 2*k*pi

pi/4 + x = +/-pi/4 +
2kpi

We'll solve the 1st case:

pi/4 + x
= pi/4 + 2kpi

x = 2kpi

We'll solve the
2nd case:

pi/4 +x = -pi/4 + 2kpi

x =
2kpi - pi/2

The solutions of the linear trigonometric
equation are:{2kpi}U{2kpi - pi/2}.<lt;/strong>