Question

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

Answer 1

Answer:

The numerical value of the trigonometric function is 30 °

Step-by-step explanation:

Given trigonometric function as :

$\frac{1 + cos x}{sin x}$ + $\frac{sin x}{1 + cos x}$ = 4

or, Taking LCM we get

$\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}$ = 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, $\frac{2 ( 1+ cos x )}{4 ( 1 + cos x )}$ = sin x

Or, sin x = $\frac{1}{2}$

∴  x = $sin^{-1}\frac{1}{2}$

 ∵ sin 30 ° = $\frac{1}{2}$

I.e  x = 30 °

Hence The numerical value of the trigonometric function is 30 °  answer