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To solve, factor out the GCF which is cosx.
Then, set each factor equal to zero and solve for x.
For the first factor,
`cos x= 0`
Since cosine function is zero when the angle is 90 and 270 degrees, then:
`x= 90^o + 360^o k` and `x=270^o + 360^o k`
Anf for the second factor,
Add both sides by 1.
Then, divide both sides by 2.
Since sine function is equal to 1/2 when the angle is 30 and 150 degrees, then:
`x=30^0+360^o k` and `x=150^0+360^o k`
Hence, the solutions of the equation 2cosx sinx-cosx=0 are:
> `x_1= 30^o + 360^o k ` ,
> `x_2=90^o + 360^o k` ,
> `x_3= 150^o + 360^o k` , and
> `x_4=270^0+360^o k`
where k is any integer.
(For problem #2 and #3, please post it as separate question in Homework Help.)
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