What is the general solution for 3cos(2x)-5cos(x)=0 ?

The general solution for 3cos(2x)-5cos(x)=0 is x=1.98675…+2pin,x=-1.98675…+2pin

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3cos(2x)-5cos(x)=0

3 cos (2 x) - 5 cos (x) = 0

x = 1.98675 \dots + 2 πn, x = - 1.98675 \dots + 2 πn

Solution steps

3 cos (2 x) - 5 cos (x) = 0

Rewrite using trig identities

(- 1 + 2 cos^{2} (x)) \cdot 3 - 5 cos (x) = 0

Solve by substitution

cos (x) = \frac{5 + 97}{12}, cos (x) = \frac{5 - 97}{12}

cos (x) = \frac{5 + 97}{12} :

No Solution

cos (x) = \frac{5 - 97}{12} : x = arccos (\frac{5 - 97}{12}) + 2 πn, x = - arccos (\frac{5 - 97}{12}) + 2 πn

Combine all the solutions

x = arccos (\frac{5 - 97}{12}) + 2 πn, x = - arccos (\frac{5 - 97}{12}) + 2 πn

Show solutions in decimal form

x = 1.98675 \dots + 2 πn, x = - 1.98675 \dots + 2 πn

sec (3 θ) - 2 = 0

sin (5 x) = - 1

tan^{2} (x) + 3 sec (x) = - 3

csc (x) = - \frac{2 3}{3}

sin (2 x) = - 5 cos (2 x), 0 \leq x \leq 2 π

What is the general solution for 3cos(2x)-5cos(x)=0 ?
The general solution for 3cos(2x)-5cos(x)=0 is x=1.98675…+2pin,x=-1.98675…+2pin