What is the general solution for (3+sin(x))^2=13-cos^2(x) ?

The general solution for (3+sin(x))^2=13-cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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(3+sin(x))^2=13-cos^2(x)

(3 + sin (x))^{2} = 13 - cos^{2} (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

(3 + sin (x))^{2} = 13 - cos^{2} (x)

Subtract

13 - cos^{2} (x)

from both sides

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

Rewrite using trig identities

- 4 + 6 sin (x) + 1 = 0

Group like terms

6 sin (x) - 4 + 1 = 0

Add/Subtract the numbers:

- 4 + 1 = - 3

6 sin (x) - 3 = 0

Move

3

to the right side

6 sin (x) = 3

Divide both sides by

6

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

General solutions for

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π

tan (2 x) = cot (3 x)

sin (x) = \infty

- e^{- s i n (x)} (sin (x) + cos^{2} (x)) = 0

cos^{2} (β) - cot^{2} (β) = cos^{2} (β) cot^{2} (β)

What is the general solution for (3+sin(x))^2=13-cos^2(x) ?
The general solution for (3+sin(x))^2=13-cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin