What is the general solution for cos^2(x)cos(x)=0 ?

The general solution for cos^2(x)cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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cos^2(x)cos(x)=0

cos^{2} (x) cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

cos^{2} (x) cos (x) = 0

Simplify

cos^{2} (x) cos (x) : cos^{3} (x)

cos^{2} (x) cos (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos^{2} (x) cos (x) = cos^{2 + 1} (x)

= cos^{2 + 1} (x)

Add the numbers:

2 + 1 = 3

= cos^{3} (x)

cos^{3} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 cos (x) = - 3

8 sec (x) - 3 tan^{2} (x) = 7

sin^{2} (6 x) + sin^{2} (3 x) = 0

\frac{1}{( 2 - sin ( x ) )} = sin (x)

6 sin (x) - 3 sin^{2} (x) = 3 - cos^{2} (x)

What is the general solution for cos^2(x)cos(x)=0 ?
The general solution for cos^2(x)cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin