Given 1+ cos x/ sin x + sin x/1+ cos x= 4, find a numerical value of one trigonometric function of x.

Answer:The numerical value of the trigonometric function is 30 ° Step-by-step explanation:Given trigonometric function as :[tex]\frac{1 + cos x}{sin x}[/tex] + [tex]\frac{sin x}{1 + cos x}[/tex] = 4or, Taking LCM we get[tex]\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}[/tex] = 4Or,  ( 1 + cos x )² + sin² x = 4 × ( sin x ) × ( 1 + cos x ) 1 + cos² x + 2 cox + sin² x = 4 sin x + 4 sin x × cos xor, (  cos² x + sin² x ) + ( 1 + 2 cos x ) = 4 sin x ( 1 + cos x )  ∵  cos² x + sin² x = 1or,  1 + 1 + 2 cos x  = 4 sin x ( 1 + cos x )or, 2 + 2 cos x = 4 sin x ( 1 + cos x )or, 2 ( 1 + cos x ) = 4 sin x ( 1 + cos x )Or, [tex]\frac{2 ( 1+ cos x )}{4 ( 1 + cos x )}[/tex] = sin xOr, sin x = [tex]\frac{1}{2}[/tex]∴  x = [tex]sin^{-1}\frac{1}{2}[/tex]  ∵ sin 30 ° = [tex]\frac{1}{2}[/tex]I.e  x = 30 °Hence The numerical value of the trigonometric function is 30 °  answer