What is the general solution for cos(4x)-7cos(2x)=8 ?

The general solution for cos(4x)-7cos(2x)=8 is x= pi/2+pin

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cos(4x)-7cos(2x)=8

cos (4 x) - 7 cos (2 x) = 8

x = \frac{π}{2} + πn

Solution steps

cos (4 x) - 7 cos (2 x) = 8

Subtract

8

from both sides

cos (4 x) - 7 cos (2 x) - 8 = 0

Rewrite using trig identities

- 9 + 2 cos^{2} (2 x) - 7 cos (2 x) = 0

Solve by substitution

cos (2 x) = \frac{9}{2}, cos (2 x) = - 1

cos (2 x) = \frac{9}{2} :

No Solution

cos (2 x) = - 1 : x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{2} + πn

6 tan (B) + 14 = 0

- 4 tan^{2} (θ) - 4 tan (θ) - 9 = 8 tan (θ) - 4

cot (4 x) = - \frac{3}{3}

sin (x) = \frac{3.9}{8.1}

5 sin (x) = - 2 cos^{2} (x) + 4

What is the general solution for cos(4x)-7cos(2x)=8 ?
The general solution for cos(4x)-7cos(2x)=8 is x= pi/2+pin