Respuesta :
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] = 4
or, Taking LCM we get
[tex]\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}[/tex] = 4
Or, ( 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 x
or, ( cos² x + sin² x ) + ( 1 + 2 cos x ) = 4 sin x ( 1 + cos x )
∵ cos² x + sin² x = 1
or, 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 x
Or, 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
