Question

If sin ( 2x+y)=cos (4x-y), then find the value of tan 3x.
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Answer 1

$\huge\dag\fbox{AnswEr️️}\dag$

We know that,

cos A = sin(90° - A)

SO,

$\longrightarrow{sin(2x + y) = cos(4x - y)}$

$\longrightarrow{sin(2x + y) = sin[90° - (4x - y)]}$

$\longrightarrow{sin(2x + y) = sin[90° - 4x + y]}$

$\longrightarrow{2x \: + \: y \: = 90° \: - 4x \: + y}$

$\longrightarrow{2x \: + \: 4x \: = \: 90° + \: y \: - \: y}$

$\longrightarrow{6x \: = \: 90°}$

$\longrightarrow \huge x =\frac{90°}{6}$

$\huge\fbox{ x = 15°}$

•NOW ,

$tan \: 3x \: = tan \: 3(15°) \\\ = 45°$

$\large\cal\colorbox{red}{So \: the \: value \: of \: tan \: 3x \: is \: 45°.}$

Answer 2

Answer:

A table of values can be used to plot the graphs of the functions y = sin x, y = cos x, and y = tan x once we have determined the sine, cosine, and tangent of any angle.

$Therefore\ tan\ 3x=tan (3 x 15\°)= tan 45\° = 1$

Step-by-step explanation:

Applications ranging from tidal movement to signal processing, which is essential in contemporary telecommunications and radio-astronomy, are based on the graphs of the sine and cosine functions, which are used to describe wave motion. This offers a spectacular illustration of how a basic concept combining geometry and ratio was abstracted and developed into a very potent tool that altered the course of human history.

$Given sin (2x+y)= cos (4x-y)$

$or, sin (2x+y)=sin (90° - (4x-y)}$

$Therefore\ 2x+y=90\° - (4x-y)$

$or, 2x+y=90\°-4x+y$

$or, 6x=90\° or, x=15\°$

$Therefore\ tan\ 3x=tan (3 x 15\°)= tan 45\° = 1$

To learn more about  graphs, visit:

https://brainly.in/question/24787101

To learn more about cosine, visit:

https://brainly.in/question/54160971

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