Hello, could you help with the interpretation of the results of solving this equation.
Solve[(Cos[f]Cos[b]+Sin[f]Cos[v])Cos[d]Cos[x]+Cos[d]Sin[x]Sin[b]Sin[v]+Sin[d](Sin[f]Cos[b]-Cos[f]Sin[f]Cos[v])==0,x]
{{x -> ConditionalExpression[
ArcTan[(-Cos[b]^2 Cos[d] Cos[f] Sin[d] Sin[f] +
Cos[b] Cos[d] Cos[f]^2 Cos[v] Sin[d] Sin[f] -
Cos[b] Cos[d] Cos[v] Sin[d] Sin[f]^2 +
Cos[d] Cos[f] Cos[v]^2 Sin[d] Sin[
f]^2 - \[Sqrt](Cos[b]^2 Cos[d]^4 Cos[f]^2 Sin[b]^2 Sin[
v]^2 + 2 Cos[b] Cos[d]^4 Cos[f] Cos[v] Sin[b]^2 Sin[
f] Sin[v]^2 +
Cos[d]^4 Cos[v]^2 Sin[b]^2 Sin[f]^2 Sin[v]^2 -
Cos[b]^2 Cos[d]^2 Sin[b]^2 Sin[d]^2 Sin[f]^2 Sin[v]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[b]^2 Sin[d]^2 Sin[
f]^2 Sin[v]^2 -
Cos[d]^2 Cos[f]^2 Cos[v]^2 Sin[b]^2 Sin[d]^2 Sin[f]^2 Sin[
v]^2 + Cos[d]^4 Sin[b]^4 Sin[v]^4))/(Cos[b]^2 Cos[
d]^2 Cos[f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2),
Csc[b] Csc[v] Sec[
d] (-Cos[b] Sin[d] Sin[f] + Cos[f] Cos[v] Sin[d] Sin[f] + (
Cos[b]^3 Cos[d]^2 Cos[f]^2 Sin[d] Sin[f])/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
Cos[b]^2 Cos[d]^2 Cos[f]^3 Cos[v] Sin[d] Sin[f])/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) + (
2 Cos[b]^2 Cos[d]^2 Cos[f] Cos[v] Sin[d] Sin[f]^2)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
2 Cos[b] Cos[d]^2 Cos[f]^2 Cos[v]^2 Sin[d] Sin[f]^2)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) + (
Cos[b] Cos[d]^2 Cos[v]^2 Sin[d] Sin[f]^3)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
Cos[d]^2 Cos[f] Cos[v]^3 Sin[d] Sin[f]^3)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) +
(Cos[b] Cos[d] Cos[
f] \[Sqrt](-Cos[d]^2 Sin[b]^2 Sin[
v]^2 (-Cos[b]^2 Cos[d]^2 Cos[f]^2 -
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] -
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[b]^2 Sin[d]^2 Sin[f]^2 -
2 Cos[b] Cos[f] Cos[v] Sin[d]^2 Sin[f]^2 +
Cos[f]^2 Cos[v]^2 Sin[d]^2 Sin[f]^2 -
Cos[d]^2 Sin[b]^2 Sin[v]^2)))/(Cos[b]^2 Cos[d]^2 Cos[
f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[d]^2 Sin[b]^2 Sin[v]^2) + (Cos[d] Cos[v] Sin[
f] \[Sqrt](-Cos[d]^2 Sin[b]^2 Sin[
v]^2 (-Cos[b]^2 Cos[d]^2 Cos[f]^2 -
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] -
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[b]^2 Sin[d]^2 Sin[f]^2 -
2 Cos[b] Cos[f] Cos[v] Sin[d]^2 Sin[f]^2 +
Cos[f]^2 Cos[v]^2 Sin[d]^2 Sin[f]^2 -
Cos[d]^2 Sin[b]^2 Sin[v]^2)))/(Cos[b]^2 Cos[d]^2 Cos[
f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[d]^2 Sin[b]^2 Sin[v]^2))] + 2 \[Pi] C[1],
C[1] \[Element] Integers]}, {x ->
ConditionalExpression[
ArcTan[(-Cos[b]^2 Cos[d] Cos[f] Sin[d] Sin[f] +
Cos[b] Cos[d] Cos[f]^2 Cos[v] Sin[d] Sin[f] -
Cos[b] Cos[d] Cos[v] Sin[d] Sin[f]^2 +
Cos[d] Cos[f] Cos[v]^2 Sin[d] Sin[
f]^2 + \[Sqrt](Cos[b]^2 Cos[d]^4 Cos[f]^2 Sin[b]^2 Sin[
v]^2 + 2 Cos[b] Cos[d]^4 Cos[f] Cos[v] Sin[b]^2 Sin[
f] Sin[v]^2 +
Cos[d]^4 Cos[v]^2 Sin[b]^2 Sin[f]^2 Sin[v]^2 -
Cos[b]^2 Cos[d]^2 Sin[b]^2 Sin[d]^2 Sin[f]^2 Sin[v]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[b]^2 Sin[d]^2 Sin[
f]^2 Sin[v]^2 -
Cos[d]^2 Cos[f]^2 Cos[v]^2 Sin[b]^2 Sin[d]^2 Sin[f]^2 Sin[
v]^2 + Cos[d]^4 Sin[b]^4 Sin[v]^4))/(Cos[b]^2 Cos[
d]^2 Cos[f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2),
Csc[b] Csc[v] Sec[
d] (-Cos[b] Sin[d] Sin[f] + Cos[f] Cos[v] Sin[d] Sin[f] + (
Cos[b]^3 Cos[d]^2 Cos[f]^2 Sin[d] Sin[f])/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
Cos[b]^2 Cos[d]^2 Cos[f]^3 Cos[v] Sin[d] Sin[f])/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) + (
2 Cos[b]^2 Cos[d]^2 Cos[f] Cos[v] Sin[d] Sin[f]^2)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
2 Cos[b] Cos[d]^2 Cos[f]^2 Cos[v]^2 Sin[d] Sin[f]^2)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) + (
Cos[b] Cos[d]^2 Cos[v]^2 Sin[d] Sin[f]^3)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 + Cos[d]^2 Sin[b]^2 Sin[v]^2) - (
Cos[d]^2 Cos[f] Cos[v]^3 Sin[d] Sin[f]^3)/(
Cos[b]^2 Cos[d]^2 Cos[f]^2 +
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[d]^2 Sin[b]^2 Sin[
v]^2) - (Cos[b] Cos[d] Cos[
f] \[Sqrt](-Cos[d]^2 Sin[b]^2 Sin[
v]^2 (-Cos[b]^2 Cos[d]^2 Cos[f]^2 -
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] -
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[b]^2 Sin[d]^2 Sin[f]^2 -
2 Cos[b] Cos[f] Cos[v] Sin[d]^2 Sin[f]^2 +
Cos[f]^2 Cos[v]^2 Sin[d]^2 Sin[f]^2 -
Cos[d]^2 Sin[b]^2 Sin[v]^2)))/(Cos[b]^2 Cos[d]^2 Cos[
f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[d]^2 Sin[b]^2 Sin[v]^2) - (Cos[d] Cos[v] Sin[
f] \[Sqrt](-Cos[d]^2 Sin[b]^2 Sin[
v]^2 (-Cos[b]^2 Cos[d]^2 Cos[f]^2 -
2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] -
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[b]^2 Sin[d]^2 Sin[f]^2 -
2 Cos[b] Cos[f] Cos[v] Sin[d]^2 Sin[f]^2 +
Cos[f]^2 Cos[v]^2 Sin[d]^2 Sin[f]^2 -
Cos[d]^2 Sin[b]^2 Sin[v]^2)))/(Cos[b]^2 Cos[d]^2 Cos[
f]^2 + 2 Cos[b] Cos[d]^2 Cos[f] Cos[v] Sin[f] +
Cos[d]^2 Cos[v]^2 Sin[f]^2 +
Cos[d]^2 Sin[b]^2 Sin[v]^2))] + 2 \[Pi] C[1],
C[1] \[Element] Integers]}}