Question

find the general solution of the equation : Cosx = 0​

Answer 1

Let us find the general solutions of  cos x = 0.

Now cos-1 0 = π/2

Hence the general solution is

x = ±π/2 + 2kπ, where k is any integer.

 

Let us find the general solutions of  tan x = 0.

Now  

Hence the general solution is

x = kπ, where k is any integer.

 

Let us find the general solutions of  .

The equation is equivalent to .

Now  

Hence the general solution is

x = π/4 +2kπ or x = 3π/4 +2kπ, where k is any integer.

 

Let us find the general solutions of  sin x = cos x.

The equation is equivalent to , which can be simplified to .

Now  

Hence the general solution is

x = π/4 +kπ, where k is any integer.

 

Let us find the general solutions of  2cos2x = cos x (ie cos x(2cos x – 1)=0 .

The equation is equivalent to  2cos2x − cos x = 0  which can be factorised to   cos x(2cos x – 1) = 0

If  cos x = 0, then consider   cos-1(0)= π/2.

Hence a solution is   x = ±π/2 + 2kπ

If   2cos x – 1 = 0, this equation is equivalent to  

Now  

Hence a solution is   x = ± π/3 + 2kπ

Therefore the general solution is

x = ±π/3 +2kπ or x = ±π/2 +2kπ, where k is any integer.

 

Let us find the general solutions of  2sin x = -1.

The equation is equivalent to .

Now  

and also -5π/6. Hence the general solution is

x = -π/6 +2kπ or x = -5π/6 +2kπ, where k is any integer.

Answer 2

Answer:

x=90

since cos90=0

if you want any explanation tell me i ll comment in the answer