Question

f(x) = sin4x + sin3x+ sin2x / cos4x + cos3x+ cos2x
Find the domain of f

Answer 1

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Answer:

all values of x except π /6 + πn/3  &  2π/3 + πn

Step-by-step explanation:

domain of function f(x)sin4x+sin3x+sin2x/cos 4x+cos3x+cos2x

Using sin a + sin b = 2sin((a+b)/2)cos((a-b)/2

sin4x + sin2x = 2sin3xcosx

Using cos a + cosb = 2cos((a+b)/2)cos((a-b)/2

cos4x + cos2x = 2cos3xcosx

putting these values in f(x)

(2sin3xcox + sin3x) / (2cos3xcosx + cos3x)

f(x)  = (sin3x(2cosx+1))/(cos3x(2cosx+1))

cancelling 2cosx +1

so 2cosx +1 not equal to 0

=  sin3x/cos3x

so cos3x ≠ 0

so cos 3x is real all for real numbers except the values where 3x is equal to π /2 + πn for all integer values of n

x is not equal to π /6 + πn/3

2cosx +1 ≠ 0

cos x  ≠ -1/2

x not equal to 2π/3 + πn

domain of function is all values of x except

π /6 + πn/3  &  2π/3 + πn

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Answer 2

Answer:

all values of x except π /6 + πn/3 & 2π/3 + πn

Step-by-step explanation:

domain of function

f(x)sin4x+sin3x+sin2x/cos 4x+cos3x+cos2x

Using sin a + sin b = 2sin((a+b)/2)cos((a-b)/2

sin4x + sin2x = 2sin3xcosx

Using cos a + cosb = 2cos((a+b)/2)cos((a-b)/2

cos4x + cos2x = 2cos3xcosx

putting these values in f(x)

(2sin3xcox + sin3x) / (2cos3xcosx + cos3x)

f(x)  = (sin3x(2cosx+1))/(cos3x(2cosx+1))

cancelling 2cosx +1

so 2cosx +1 not equal to 0

=  sin3x/cos3x

so cos3x ≠ 0

so cos 3x is real all for real numbers except the values where 3x is equal to π /2 + πn for all integer values of n

x is not equal to π /6 + πn/3

2cosx +1 ≠ 0

cos x  ≠ -1/2

x not equal to 2π/3 + πn

domain of function is all values of x except

π /6 + πn/3  &  2π/3 + πn