Question

Use trigonometric identities to solve each equation within the given domain.

4cos4(x) – 5cos2(x) + 1 = 0 from [0, 2π). PLEASE SHOW WORK!!!

Answer 1

4cos ^4(x) -5cos^2(x)+1=0

(u^-1) (4u^-1)=0

(u^-1)=0

u^=1

u=√1

u=1

u=±1

cos (x)=±1

x=0 or π

4u^-1=0

4u^=1

u^=1/4

u=√1/4

u=1/2

u= ±1/2

cos (x)=±1/2

x= π/3 or 4π/3

x= 0, π/3, π, 4π/3