What is the general solution for 5cos(x)=1+2sin^2(x) ?

The general solution for 5cos(x)=1+2sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin

Popular >

5cos(x)=1+2sin^2(x)

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

1 + 2 sin^{2} (x)

from both sides

5 cos (x) - 1 - 2 sin^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - 3

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (2 x + 1) = - cot (x + 3)

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

tan (x) + tan^{3} (x) = 0

sin^{3} (x) - 2 sin (x) = 4 cos^{2} (x) - 3

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

What is the general solution for 5cos(x)=1+2sin^2(x) ?
The general solution for 5cos(x)=1+2sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin