What is the general solution for 5-5cos(x)=4sin^2(x) ?

The general solution for 5-5cos(x)=4sin^2(x) is x=2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin

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5-5cos(x)=4sin^2(x)

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

x = 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

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

Subtract

4 sin^{2} (x)

from both sides

5 - 5 cos (x) - 4 sin^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = \frac{1}{4}

cos (x) = 1 : x = 2 πn

cos (x) = \frac{1}{4} : x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

3 cot^{2} (x) - 14 csc (x) - 2 = 0

250 = 100 \cdot 5 \cdot cos (x)

cos (θ) = - \frac{2}{5}

tan (x) = \frac{1}{sin ( 2 x )}, 0 \leq x \leq π

cos (x) = 9054

What is the general solution for 5-5cos(x)=4sin^2(x) ?
The general solution for 5-5cos(x)=4sin^2(x) is x=2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin