find general solution?

Question

find general solution
find the general solution of the equation
cos(x-7)=2cos(x-7)
giving the answer correct to the nearest 0.1degree.
7 is the degree.

Answer 1

set y = x-7 for convenience.

sin(y) = 2sin(y)

<=> sin(y) = 0 <=> y = 0 + k180, k = ...,-1,0,1,...
<=> x - 7 = k180 <=> x = 7 + k180, k = ...,-1,0,1,...

Answer 2

If this is one of the trigonometrical equation and the angles are all measured in degrees then :

cos (x-7) = 2cos(x-7)
becomes cos (x-7) =0 =cos 90
Then the general solution is x-7 = 180n + 90 = (2n +1) 90 degrees (where n=...-2,-1,0,1,2,...)

or x = (2n+1) 90 + 7 degrees
or may also be written as x= 180n + 97 degrees.
where n = ... -2,-1,0,1,2,...

Answer 3

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Answer 4

cos(x-7)=2cos(x-7)
=> cos(x-7)[1-2] = 0
=>cos(x-7)=0

=> x = 97+n180 where n is an integer

Answer 5

cos(x-7)=0 and the general solution for cosx =0 will be(2n+1)*pi/2
so x-7=(2n+1)*pi/2 and so x= (2n+1)*pi/2+7*pi/180 in radians
in degress it will be (2n+1)*90*+7*=n(180*)+97*

Answer 6

if you go to www.quickmath.com

x = 7 + (pi/2)
x = 7 - (pi/2)

or

x = 97°
x = -83°

Answer 7

that is cos(x-7) = 0
x -7 = (2n+1) pi/2
n ftom -inf to _inf
x = 7+(2n+1)/pi/2

Answer 8

x=((plus or minus (2*n+1)*pi/2)+7*pi/180) in radiance; n=0,1,2,3,.....................

Answer 9

0.7