Solve cosx tanx=1/2 ? Thanks !

Question

Question

Solve cosx tanx=1/2 ? Thanks !

Solve

cosx tanx=1/2 ?

Thanks !

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Answer 1

Answer #1

Hi..

First, simplify the left side of the equation using the trigonometric identity for tangent:

tangg_ cose

cosx tanx will become

sinc coS.sinc

Then, the simplified equation we now have to solve is

mathImg.php?%5Cdisplaystyle%7B%5Csin%7B%

The values of angle x which sign equals 1/2 are 30 degrees and 150 degrees, or $mathImg.php?%5Cdisplaystyle%5Cfrac%7B%5C$ and $mathImg.php?%5Cdisplaystyle%5Cfrac%7B%7B$ radians.

Since sine is a periodic function with the period of mathImg.php?%5Cdisplaystyle%7B2%7D%5Cpi , any angle obtained by adding an integer multiple of to $mathImg.php?%5Cdisplaystyle%5Cfrac%7B%5C$ and $mathImg.php?%5Cdisplaystyle%5Cfrac%7B%7B$ will have the same sine.

So, all solutions of this equation are

and ,

where k is an integer:

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Answer 2

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