sec + tan = cos /(1 + sin)
sec and tan are defined so cos is non-zero.
1/cos + sin/cos = cos/(1 + sin)
(1 + sin)/cos = cos/(1 + sin)
cross-multiplying, (1 + sin)2 = cos2
(1 + sin)2 = 1 - sin2
1 + 2sin + sin2 = 1 - sin2
2sin2 + 2sin = 0
sin2 + sin = 0
sin(sin + 1) = 0
so sin = 0 or sin = -1
But sin = -1 implies that cos = 0 and cos is non-zero.
Therefore sin = 0 or the solutions are k*pi radians where k is an integer.
either cos OR tan-sin equals zero socos=0 at pi/2 and 3pi/2ortan=sin which is impossibleim not sure though
No, but cos(-x) = cos(x), because the cosine function is an even function.
Sin 15 + cos 105 = -1.9045
A*sin(x) + cos(x) = 1B*sin(x) - cos(x) = 1Add the two equations: A*sin(x) + B*sin(x) = 2(A+B)*sin(x) = 2sin(x) = 2/(A+B)x = arcsin{2/(A+B)}That is the main solution. There may be others: depending on the range for x.
3cos
1
either cos OR tan-sin equals zero socos=0 at pi/2 and 3pi/2ortan=sin which is impossibleim not sure though
No, but cos(-x) = cos(x), because the cosine function is an even function.
Sin 15 + cos 105 = -1.9045
A*sin(x) + cos(x) = 1B*sin(x) - cos(x) = 1Add the two equations: A*sin(x) + B*sin(x) = 2(A+B)*sin(x) = 2sin(x) = 2/(A+B)x = arcsin{2/(A+B)}That is the main solution. There may be others: depending on the range for x.
sec(x)=1/cos(x), by definition of secant.
3cos
leonhard euler
The principal solution for sin(A + 5) = cos(3A - 25), with angles measured in degrees, is A = 15 degrees.
[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1]iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1iff -cos^2 = sin^2 - 11 = sin^2 + cos^2, which is true,
cos x - 0.5 = 0 ⇒ cos x = 0.5 ⇒ x = 2nπ ± π/3
2