What is the general solution for cos(x)+9sin^2(x)=1 ?

The general solution for cos(x)+9sin^2(x)=1 is x=2.66571…+2pin,x=-2.66571…+2pin,x=2pin

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cos(x)+9sin^2(x)=1

cos (x) + 9 sin^{2} (x) = 1

x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn, x = 2 πn

Solution steps

cos (x) + 9 sin^{2} (x) = 1

Subtract

1

from both sides

cos (x) + 9 sin^{2} (x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = - \frac{8}{9}, cos (x) = 1

cos (x) = - \frac{8}{9} : x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn, x = 2 πn

Show solutions in decimal form

x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn, x = 2 πn

- \frac{2}{3} cos (x) + \frac{2}{3} cos (2 x) = 0

sin (θ) - cos (θ) = 0

cot (3 x) = - 3, 0 \leq x \leq 2 π

3 cos^{2} (x) + sin^{2} (x) = 3

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

What is the general solution for cos(x)+9sin^2(x)=1 ?
The general solution for cos(x)+9sin^2(x)=1 is x=2.66571…+2pin,x=-2.66571…+2pin,x=2pin