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: D. sin x= 1/2

Explanation:

Edg 2020

Answer 2

The numerical value of the trigonometric function is 30 °

Explanation:

Given trigonometric function as :

`(1 + cos x)/(sin x)` +
`(sin x)/(1 + cos x)` = 4

or, Taking LCM we get

`((1+cosx)^(2)+sin^(2)x)/((sinx)* (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,
`(2 ( 1+ cos x ))/(4 ( 1 + cos x ))` = sin x

Or, sin x =
`(1)/(2)`

∴ x =
`sin^(-1)(1)/(2)`

∵ sin 30 ° =
`(1)/(2)`

I.e x = 30 °

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