Question

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

Answer 1

Answer:

Step-by-step explanation:

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

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

sin4x + sin2x = 2sin3xcosx

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

cos4x + cos2x = 2cos3xcosx

putting these values

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

= (sin3x(2cosx+1))/(cos3x(2cosx+1))
cancelling 2cosx +1
so 2cosx +1 not equal to 0
= sin3x/cos3x

= tan3x

tan3x is real when cos3x not equal to 0
so tan 3x is real all for real numbers except the values where 3x is equal to , the values π /2 + πn for all integer values of n

x is not equal to π /6 + πn/3

2cosx +1 not equal to 0
cos x not equal to -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

Answer 2

sorry I can't do it I will try my best